#engineering

Rigid-body rotational-inertia mechanics as an API, computed locally and deterministically. The shape endpoint returns the mass moment of inertia and the radius of gyration k = √(I/m) for a named standard body about its characteristic axis — a solid sphere (I = 2/5·m·r²), thin spherical shell (2/3·m·r²), solid cylinder or disk (1/2·m·r²), annular/hollow cylinder (1/2·m·(r1²+r2²)), thin ring (m·r²), thin rod about its centre (1/12·m·l²) or about one end (1/3·m·l²), rectangular plate or cuboid (1/12·m·(a²+b²)), solid cone (3/10·m·r²) and point mass (m·r²) — so a 2 kg solid sphere of radius 0.5 m has I = 0.2 kg·m². The parallel-axis endpoint applies the Steiner theorem I = I_cm + m·d² to shift a moment of inertia from the centre-of-mass axis to any parallel axis a distance d away. The shapes endpoint lists the whole catalog with its formulas. All quantities are SI (kg, m → kg·m²). Everything is computed locally and deterministically, so it is instant and private. Ideal for mechanical-engineering, robotics, CAD/CAE, rotating-machinery, structural-dynamics and physics-education app developers, flywheel-and-shaft design tools, and simulation software. Pure local computation — no key, no third-party service, instant. Live, nothing stored. 3 endpoints. This is rotational inertia; for stored rotational energy and flywheel sizing use a flywheel API and for torque and angular acceleration a torque API.

api.oanor.com/momentofinertia-api

Geometria de conicidade e cone como uma API, computada local e deterministicamente. O endpoint de conicidade relaciona os diâmetros grande e pequeno, o comprimento e a conicidade de uma peça cônica: forneça os dois diâmetros e o comprimento e ele retorna a razão de conicidade, a conicidade por pé e por polegada (para peças em polegadas), o ângulo incluído 2·atan((D−d)/(2L)) e o ângulo (de conicidade) metade a partir do eixo — ou deixe um dos diâmetros ou o comprimento de fora e forneça a conicidade por pé, e ele resolve para a dimensão faltante. O endpoint diâmetro-em fornece o diâmetro (e raio) em qualquer distância ao longo da conicidade, medido a partir da extremidade grande ou pequena, por interpolação linear d(x) = D − (D−d)·x/L. O endpoint morse é uma referência da série padrão de conicidade Morse MT0 a MT7, com a conicidade por pé de cada cone, diâmetro grande e pequeno na linha de calibre, comprimento e ângulo incluído. Comprimentos e diâmetros usam unidades consistentes (polegadas por padrão, ou milímetros para as saídas de ângulo e razão). Tudo é computado local e deterministicamente, então é instantâneo e privado. Ideal para aplicações de usinagem e ferramentas de torno, CAD e fabricação de ferramentas, projetos de fabricação e metalurgia, e calculadoras de engenharia mecânica. Computação local pura — sem chave, sem serviço de terceiros, instantâneo. Ao vivo, nada armazenado. 3 endpoints. Isto é geometria de conicidade; para passo de rosca e broca de rosca use uma API de rosca e para geometria de engrenagens de dentes retos use uma API de engrenagens.

api.oanor.com/taper-api

Thermal-expansion maths as an API, computed locally and deterministically. The linear endpoint computes how much a solid grows or shrinks when its temperature changes, ΔL = α·L0·ΔT, returning the change in length and the new length from an original length, a temperature change (given directly or as an initial and final temperature) and the linear expansion coefficient α — taken from a built-in material table (steel, aluminium, copper, concrete, glass, invar and more) or supplied directly; lengths accept metres, centimetres, millimetres, feet or inches. The volume endpoint computes volumetric expansion, ΔV = β·V0·ΔT, where for a solid the volumetric coefficient is β ≈ 3α and for a liquid (water, ethanol, mercury, petrol and others) β is taken directly; volumes accept cubic metres, litres, millilitres or cubic feet. The materials endpoint lists the coefficients. A negative temperature change gives contraction. Everything is computed locally and deterministically, so it is instant and private. Ideal for civil and mechanical engineering tools, rail, pipe and bridge expansion-gap design, manufacturing-tolerance and HVAC apps, and physics education. Pure local computation — no key, no third-party service, instant. Live, nothing stored. 3 endpoints. This is thermal expansion; for heat energy and temperature change use a specific-heat API.

api.oanor.com/thermalexpansion-api

Power-screw (lead-screw and screw-jack) mechanics as an API, computed locally and deterministically. The torque endpoint computes the torque to raise and to lower a load on a power screw from the load, the mean thread diameter, the lead (given directly or as pitch × starts) and the coefficient of friction: T_raise = (W·dm/2)·(L + π·μ′·dm)/(π·dm − μ′·L), with the matching lower torque, the lead angle, the efficiency (W·L ÷ 2π·T_raise) and whether the screw is self-locking (it is when the effective friction is at least the tangent of the lead angle). Square threads are the default; pass a thread angle (for example 29° for an ACME thread) and it applies the effective friction μ/cos(half-angle). The effort endpoint turns that torque into the hand force on a lever or handle and the resulting mechanical advantage. The travel endpoint relates turns, lift distance and — with an rpm — the linear speed and time. Lengths are in millimetres, load in newtons and torque in newton-metres. Everything is computed locally and deterministically, so it is instant and private. Thread friction only — add collar/thrust friction separately. Ideal for machine-design and mechanism tools, jack, press, vice and clamp design, maker and robotics projects, and engineering calculators. Pure local computation — no key, no third-party service, instant. Live, nothing stored. 3 endpoints. This is power-screw mechanics; for the geometry of a screw thread use a thread API and for bolt tightening torque use a torque API.

api.oanor.com/screwjack-api

Weld design maths as an API, computed locally and deterministically. The fillet endpoint sizes an equal-leg fillet weld: from the leg size, the weld length and an allowable shear stress it returns the effective throat (leg ÷ √2), the effective area, the load capacity and the strength per millimetre of weld; give a design force instead of a leg and it returns the required throat and leg size, and if you also pass a provided leg it reports the utilization and whether the weld is adequate. The butt endpoint handles a full-penetration butt (groove) weld, where the effective throat equals the plate thickness, returning the area and capacity. The throat endpoint converts between leg and throat — equal-leg (throat = leg ÷ √2), unequal legs (throat = a·b ÷ √(a²+b²)) and throat back to leg. Lengths are in millimetres, stress in megapascals and force in newtons. Everything is computed locally and deterministically, so it is instant and private. An estimating aid, not a code-stamped design — use the allowable stress and electrode from your governing code (AISC, Eurocode). Ideal for structural and fabrication tools, weld-design and estimating apps, maker and metalwork projects, and engineering calculators. Pure local computation — no key, no third-party service, instant. Live, nothing stored. 3 endpoints. This is weld strength sizing; for bolt tightening torque use a torque API and for the weight of the steel use a metal-weight API.

api.oanor.com/weld-api

Catenary (hanging-cable) maths as an API, computed locally and deterministically. The sag endpoint solves the exact catenary for a cable hung between two level supports: from the span, the weight per unit length and either the horizontal tension or the sag, it returns the catenary parameter a = H/w, the sag a·(cosh(L/2a) − 1), the cable length 2a·sinh(L/2a), the minimum tension (the horizontal tension at the lowest point) and the maximum tension at the supports (H·cosh(L/2a)), plus the slack over the straight span. The parabolic endpoint gives the shallow-sag parabolic approximation — sag = w·L²/(8·H) — that is standard for overhead utility lines, and converts between sag and tension either way. The length endpoint returns the cable length for a given span and sag, with the parabolic value alongside for comparison. Forces and lengths are unit-agnostic but must be consistent (for example newtons, newtons per metre and metres). Everything is computed locally and deterministically, so it is instant and private. Ideal for power-line and transmission tools, zip-line and rigging apps, suspension and surveying calculators, and physics and engineering education. Pure local computation — no key, no third-party service, instant. Live, nothing stored. 3 endpoints. This is hanging-cable catenary maths; for rigging working load limits use a rigging API and for beam deflection use a beam API.

api.oanor.com/catenary-api

Fluid-statics maths as an API, computed locally and deterministically. The pressure endpoint computes the pressure at a depth in a fluid — the gauge pressure ρ·g·h and the absolute pressure (gauge plus atmospheric) — in pascals, kilopascals, bar, psi and atmospheres, for water, seawater, oil, mercury and more, or a custom density; depths accept metres, feet or centimetres, which makes it handy for diving (about 10 m of seawater adds one atmosphere). The force endpoint computes the resultant hydrostatic force on a submerged vertical rectangular surface — an aquarium wall, a tank side, a dam face or a flood gate — as F = ρ·g·h_c·A from its width and the top and bottom depths, and gives the depth of the centre of pressure, which sits below the centroid. The buoyancy endpoint applies Archimedes' principle, F_b = ρ_fluid·g·V, to give the buoyant force and the displaced mass, and — if you supply the object's density or mass — tells you whether it floats or sinks and what fraction sits below the waterline. Everything is computed locally and deterministically, so it is instant and private. Ideal for civil and marine engineering tools, diving and aquarium apps, tank and dam design, and physics education. Pure local computation — no key, no third-party service, instant. Live, nothing stored. 3 endpoints. This is fluid statics; for pump power and head use a pump API and for pipe flow rate use a pipe-flow API.

api.oanor.com/hydrostatic-api

Sheet-metal bending maths as an API, computed locally and deterministically. The bend-allowance endpoint computes the bend allowance, bend deduction and outside setback for a single bend from the material thickness, the inside bend radius, the bend angle and the K-factor: the bend allowance is BA = θ·(r + K·t), the outside setback is OSSB = (r + t)·tan(θ/2) and the bend deduction is BD = 2·OSSB − BA, with the neutral-axis position reported too. The flat-length endpoint computes the flat blank length you need to cut: from a list of outside (mold-line) flange lengths, or two flanges, or a total, it subtracts the bend deduction for each bend. The kfactor endpoint lists typical K-factors by material — aluminium around 0.33, mild steel 0.44, stainless 0.45 — and estimates a K-factor from the inside-radius-to-thickness ratio. The K-factor can be given directly or chosen by material, and if the inside radius is omitted it defaults to the thickness. Lengths are unit-agnostic — the output matches whatever unit you supply. Everything is computed locally and deterministically, so it is instant and private. Ideal for sheet-metal CAD/CAM and press-brake tools, fabrication and unfolding apps, maker and prototyping projects, and manufacturing calculators. Pure local computation — no key, no third-party service, instant. Live, nothing stored. 3 endpoints. This is sheet-metal bend development; for the weight of the blank use a metal-weight API.

api.oanor.com/sheetmetal-api

Helical compression-spring maths as an API, computed locally and deterministically. The rate endpoint computes the spring rate from the wire diameter, the mean coil diameter and the number of active coils using k = G·d⁴/(8·D³·n), where the shear modulus G is taken from the material (music wire and spring steel, stainless, phosphor bronze, beryllium copper, titanium and more) or supplied directly — and it reports the rate in newtons per millimetre, newtons per metre and pounds per inch, along with the spring index C = D/d. The force endpoint relates force and deflection through F = k·x in both directions, taking the rate directly or deriving it from the geometry. The stress endpoint computes the shear stress in the wire, τ = 8·F·D·Kw/(π·d³), applying the Wahl correction factor Kw = (4C−1)/(4C−4) + 0.615/C for curvature and direct shear, and also reports the uncorrected stress. Lengths are in millimetres, force in newtons and stress in megapascals. Everything is computed locally and deterministically, so it is instant and private. A design aid — keep the spring index between about 4 and 12 and confirm against the material's allowable stress. Ideal for mechanical-design and CAD tools, spring-selection and prototyping apps, maker and robotics projects, and engineering calculators. Pure local computation — no key, no third-party service, instant. Live, nothing stored. 3 endpoints. This is helical-spring design; for beam deflection use a beam API.

api.oanor.com/springcoil-api

Spur-gear geometry as an API, computed locally and deterministically for standard full-depth involute teeth. The geometry endpoint takes a module and a number of teeth (and an optional pressure angle, default 20°) and returns the complete tooth geometry: the pitch diameter (module × teeth), the base, tip (outside) and root diameters, the addendum, dedendum, whole and working depth, the circular and base pitch, the diametral pitch and the tooth thickness — all in millimetres. The module can be given directly or derived from a diametral pitch or a circular pitch. The pair endpoint meshes two gears of the same module and returns each gear's pitch and tip diameter, the centre distance (module × (z1 + z2) ÷ 2) and the gear ratio. The module endpoint converts freely between module, diametral pitch and circular pitch, or derives the module from a pitch diameter and tooth count. Everything is computed locally and deterministically, so it is instant and private. Ideal for machine-design and CAD tools, gear and gearbox calculators, maker, robotics and 3D-printing projects, and mechanical-engineering apps. Pure local computation — no key, no third-party service, instant. Live, nothing stored. 3 endpoints. This is spur-gear geometry; for bicycle gear ratios and development use a bike-gear API and for belt-and-pulley drives use a belt-drive API.

api.oanor.com/spurgear-api

Pump power, head and affinity maths as an API, computed locally and deterministically. The power endpoint computes the power a pump needs from its flow rate, head, fluid density and efficiency: the hydraulic (water) power is ρ·g·Q·H, the shaft (brake) power is that divided by the pump efficiency, and an optional motor efficiency gives the electrical input power — all reported in watts, kilowatts and horsepower. Flow accepts litres per second or minute, cubic metres per hour or second and US gallons per minute; head accepts metres or feet; and the fluid can be water, seawater, oil, diesel and more, or a custom density. The head endpoint converts between pressure and head of fluid, H = P/(ρ·g), in both directions, across pascals, kPa, bar, psi and atmospheres. The affinity endpoint applies the pump affinity laws — flow scales with speed, head with speed squared and power with speed cubed — to predict the new operating point when you change the pump speed or trim the impeller diameter. Everything is computed locally and deterministically, so it is instant and private. Ideal for plumbing and HVAC tools, process and water-treatment engineering, irrigation and pool-pump apps, and energy-efficiency calculators. Pure local computation — no key, no third-party service, instant. Live, nothing stored. 3 endpoints. This is pump power and head maths; for flow rate from pipe diameter and velocity use a pipe-flow API and for open-channel flow use a Manning API.

api.oanor.com/pump-api

Screw-thread geometry as an API, computed locally and deterministically for the 60° ISO metric and Unified (UTS) thread form. The pitch endpoint converts between the thread pitch in millimetres and threads per inch (TPI = 25.4 ÷ pitch) and works out the lead — the distance the thread advances in one turn — from the pitch and the number of starts. The dimensions endpoint takes a nominal (major) diameter and a pitch and returns the full set of thread diameters and heights: the fundamental triangle height, the external thread height, the pitch diameter (D − 0.6495·P), the external minor diameter (D − 1.2269·P) and the internal minor diameter (D − 1.0825·P), in both millimetres and inches. The tapdrill endpoint gives the drill size for cutting an internal thread: the standard metric rule of nominal diameter minus pitch (about 75–83% thread), the resulting thread engagement, and — for a target engagement percentage — the matching drill size. Diameters accept millimetres or inches, and threads can be specified by pitch or by TPI. Everything is computed locally and deterministically, so it is instant and private. Ideal for machining and CNC tools, mechanical-design and CAD apps, maker and 3D-printing projects, and hardware and fastener catalogues. Pure local computation — no key, no third-party service, instant. Live, nothing stored. 3 endpoints. This is screw-thread geometry; for the torque to tighten a bolt use a torque API.

api.oanor.com/thread-api

Matemáticas de transmisión por correa y poleas como una API, calculadas local y determinísticamente. El endpoint de correa calcula la longitud de una correa trapezoidal abierta o correa plana a partir de los dos diámetros de polea y la distancia entre centros con L = 2C + (π/2)(D1+D2) + (D1−D2)²/(4C), y devuelve la longitud de la correa más el ángulo de contacto en cada polea; si se proporciona una rpm del conductor, también da la velocidad superficial de la correa. El endpoint de relación calcula la relación de velocidad de un par de poleas (diámetro conducido ÷ diámetro conductor, ya que N1·D1 = N2·D2): proporcione una rpm del conductor o del conducido y devuelve la otra, la relación de par y la velocidad de la correa. El endpoint de centros invierte la ecuación de longitud para encontrar la distancia entre centros para una longitud de correa objetivo, resolviendo la ecuación numéricamente. Los diámetros y distancias aceptan milímetros, centímetros, metros, pulgadas o pies, y las longitudes se informan en varias unidades. Todo se calcula local y determinísticamente, por lo que es instantáneo y privado. Ideal para herramientas de diseño de máquinas y trenes de transmisión, aplicaciones de mantenimiento y MRO, proyectos de fabricación y CNC, y calculadoras de ingeniería mecánica. Cálculo local puro — sin clave, sin servicio de terceros, instantáneo. En vivo, nada almacenado. 3 endpoints. Esta es transmisión de potencia por correa y polea; para relaciones de engranajes de bicicleta y desarrollo use una API de engranajes de bicicleta y para torque de apriete de pernos use una API de torque.

api.oanor.com/beltdrive-api

Roof snow-load maths as an API, computed locally and deterministically using the ASCE 7 method. The roof endpoint turns a ground snow load into the design roof snow load: the flat-roof load is pf = 0.7 · Ce · Ct · Is · pg, using the exposure, thermal and importance factors, and the sloped-roof load is ps = Cs · pf, where the slope factor Cs follows the warm-roof all-surfaces curve (1.0 up to 30°, falling linearly to 0 at 70°) or a value you supply. It reports every load in kilopascals, pascals, pounds per square foot and kilograms per square metre, and — if you give a roof area — the total load in kilonewtons, kilograms, tonnes and pounds. The depth endpoint converts a measured snow depth and a density (given directly or by snow type, from fresh ~100 to ice ~917 kg/m³) into a load. The convert endpoint converts a snow load between kPa, psf, kg/m², Pa and psi. Depths accept millimetres, centimetres, metres, inches or feet. Everything is computed locally and deterministically, so it is instant and private. An engineering aid, not a code-stamped design — always confirm against the governing local code with a qualified engineer. Ideal for structural and roofing tools, building-code and permitting apps, solar-install and carport planners, and winter-risk calculators. Pure local computation — no key, no third-party service, instant. Live, nothing stored. 3 endpoints. This is roof snow-load engineering; for roof pitch and area geometry use a roofing API and for beam reactions use a beam API.

api.oanor.com/snowload-api

Metal stock weight and cost as an API, computed locally and deterministically. The weight endpoint computes the mass of a length of metal stock from its shape, dimensions and material: round bar, square bar, flat bar or plate, sheet, hexagonal bar, round tube or pipe and rectangular (box) tube. It works out the cross-sectional area, multiplies by the length and the material density, and returns the weight per piece and the total for a quantity — in kilograms, pounds, grams and tonnes — along with the volume. Material density is looked up from a built-in table of metals (steel, stainless, aluminium, copper, brass, bronze, lead, zinc, titanium, nickel, gold, silver and more) or you can pass an explicit density. The cost endpoint multiplies that weight by a price per kilogram, pound or tonne to give the material cost per piece and in total. The materials endpoint lists the densities. Dimensions accept millimetres, centimetres, metres, inches or feet. Everything is computed locally and deterministically, so it is instant and private. Ideal for metal fabrication and machine-shop tools, engineering and CAD apps, scrap and stock quoting, and shipping-weight estimates. Pure local computation — no key, no third-party service, instant. Live, nothing stored. 3 endpoints. This is metal stock weight from geometry and density; for beam reactions and deflection use a beam API and for live metal spot prices use a commodities API.

api.oanor.com/metalweight-api

Beam statics as an API, computed locally and deterministically. The simply-supported endpoint analyses a beam on two supports under a point load (anywhere along the span) or a uniformly distributed load: it returns the support reactions, the maximum shear and the maximum bending moment with its location, and — if you pass the Young's modulus E and second moment of area I — the maximum deflection. The cantilever endpoint does the same for a beam fixed at one end, returning the reaction force and fixing moment, the maximum bending moment and the free-end deflection. The section endpoint gives the cross-section properties that those deflections need: the second moment of area (moment of inertia) and the section modulus for a rectangle, a solid circle or a hollow circular pipe. Every result lists the formula used, so you can show your working. Use consistent units — in SI, load in newtons, distributed load in N/m, lengths in metres, E in pascals and I in m⁴ give moments in N·m and deflections in metres. Everything is computed locally and deterministically, so it is instant and private. Linear-elastic, small-deflection theory — a learning and estimating tool, not a substitute for a qualified structural engineer on a real design. Ideal for engineering and architecture tools, education and physics apps, maker and DIY calculators, and CAD helpers. Pure local computation — no key, no third-party service, instant. Live, nothing stored. 3 endpoints. This is structural beam statics; for bolt and fastener torque use a torque API.

api.oanor.com/beam-api

Pipe-flow maths as an API, computed locally and deterministically. The flow endpoint relates the three quantities of pipe flow — volumetric flow rate, fluid velocity and pipe diameter — through the continuity relation Q = A·v (with A = π/4·D²): give any two and it returns the third, with the flow rate expressed in litres per second and minute, cubic metres per hour, US gallons per minute and cubic feet per minute, plus the velocity and the pipe cross-section. The reynolds endpoint computes the Reynolds number from velocity, diameter and the fluid (water, air, oil and more, or a custom kinematic viscosity) and classifies the flow as laminar, transitional or turbulent. The convert endpoint converts a flow rate between litres per second and minute, cubic metres per hour, US gallons per minute, cubic feet per minute and per second. Everything is computed locally and deterministically, so it is instant and private. It is computed in SI internally; Reynolds uses the kinematic viscosity at about 20°C. Ideal for plumbing and HVAC tools, pump and irrigation sizing, process and fluid-engineering software, and hydraulics calculators. Pure local computation — no key, no third-party service, instant. Live, nothing stored. 3 endpoints. This is fluid flow in pipes; for plain volume or unit conversion use a unit-conversion API.

api.oanor.com/flowrate-api

Bolt and fastener torque maths as an API, using the standard short-form relation T = K · D · F — torque equals the nut factor times the bolt diameter times the clamp load (preload). The torque endpoint computes the tightening torque, in newton-metres, foot-pounds, inch-pounds and kilogram-force metres, from the bolt diameter, the target clamp load and a nut factor — given directly or chosen from a condition preset (dry, lubricated, zinc-plated, galvanized, waxed and more). The preload endpoint solves the inverse: the clamp load a given torque produces on a bolt of a given diameter and friction. The convert endpoint converts a torque value between newton-metres, foot-pounds, inch-pounds and kilogram-force metres. Everything is computed locally and deterministically, so it is instant and private. The K·D·F short form is an estimate that depends heavily on friction — it is engineering guidance only, so always follow the manufacturer's torque specification. Ideal for mechanical, automotive and aerospace tools, maker and assembly apps, maintenance and field-service software, and engineering calculators. Pure local computation — no key, no third-party service, instant. Live, nothing stored. 3 endpoints. This is fastener torque; for wire gauge and resistance use a wire-gauge API and for Ohm's law use an electronics API.

api.oanor.com/torque-api

Scientific number representation as an API. The scientific endpoint expresses a number in both scientific notation (one digit before the decimal point × a power of ten) and engineering notation (the exponent a multiple of three, lining up with SI prefixes), and reports the mantissa and exponent. The sigfigs endpoint rounds a number to a chosen number of significant figures, and counts the significant figures in a value — respecting the rules for leading zeros, trailing zeros and the decimal point, and flagging the ambiguous cases such as "1200". The si-prefix endpoint formats a number with the right metric prefix (1500 → 1.5 k, 2.3×10⁹ → 2.3 G, 0.0023 → 2.3 m) with an optional unit, and parses a prefixed value back to a plain number (2.2 MΩ → 2,200,000). Everything is computed locally and deterministically, so it is instant and private. Ideal for science and engineering tools, lab and measurement software, electronics and signal work, and education. Pure local computation — no key, no third-party service, instant. Live, nothing stored. 4 endpoints. This is scientific number representation; for locale number formatting use a number-format API and for number-to-words or Roman numerals use a number API.

api.oanor.com/sigfig-api

Las constantes físicas fundamentales NIST CODATA 2022 como una API — 355 cantidades utilizadas en toda la física e ingeniería. Busque cualquier constante por nombre o slug (por ejemplo, velocidad de la luz en el vacío → 299792458 m/s, exacto; constante de Planck, carga elemental, constante de Avogadro, constante de Boltzmann, constante de gravitación newtoniana), busque por palabra clave, o enumérelas todas. Cada registro lleva el valor recomendado, la incertidumbre estándar, la unidad SI y si el valor es exacto (por definición desde la redefinición del SI de 2019). Ideal para calculadoras científicas, software de física/ingeniería, educación y herramientas de laboratorio.

api.oanor.com/constants-api