Principal stresses & Mohr circle
API · /mohr-api
Mohr Circle Stress API
healthy
4,502 Subscribers
Mohr's circle and 2D (plane) stress transformation as an API, computed locally and deterministically. The principal endpoint takes a plane-stress state — the normal stresses σx and σy and the shear stress τxy — and returns the principal stresses σ1 and σ2 = (σx+σy)/2 ± √(((σx−σy)/2)² + τxy²), the maximum in-plane shear stress, the orientation of the principal and maximum-shear planes, the centre and radius of Mohr's circle, and the von Mises and Tresca equivalent stresses (treating plane stress with the third principal σ3 = 0). The transform endpoint rotates the stress state onto a plane at any angle θ, returning σx', σy' and τx'y' using the standard transformation equations, and confirms the σx+σy invariant. The safety endpoint computes the factor of safety against a material's yield strength under either the von Mises (distortion-energy) or the Tresca (maximum-shear) criterion, from a full stress state or from principal stresses directly. Everything is computed locally and deterministically, so it is instant and private. Ideal for mechanical, structural and aerospace engineering tools, finite-element pre- and post-processing, machine-design and stress-analysis apps, and engineering education. Pure local computation — no key, no third-party service, instant. Live, nothing stored. 3 endpoints. This is stress-state analysis; for fillet-weld throat sizing use a weld API and for helical-spring rates use a spring API.
api.oanor.com/mohr-api
API health
healthy- Uptime
- 100.00%
- Server probes · 24h
- Avg latency
- 91 ms
- Server probes · 24h
- Subscribers
- 4,502
- active
- Total calls
- 36
- last 7 days
Pricing
Pick a tier — billed monthly, cancel anytime.
Free
Free
- 1,500 calls / month
- 2 requests / second
- Hard cap (429 above quota, no overage)
- Plane-stress transformation at any rotation angle
- Principal stresses + max shear
- von Mises stress output
- Deterministic, instant local compute
Starter
€9.00 /month
- 20,000 calls / month
- 5 requests / second
- Hard cap (429 above quota, no overage)
- Full Mohr's circle geometry (center, radius)
- Principal angles in deg/rad
- von Mises + Tresca equivalents
- Email support
Pro
€24.00 /month
- 150,000 calls / month
- 15 requests / second
- Hard cap (429 above quota, no overage)
- Batch stress-state evaluation
- Stress trajectory sweep across angles
- Plot-ready circle coordinates
- Higher rate limit for CAD/FEA pipelines
Mega
€74.00 /month
- 1,000,000 calls / month
- 40 requests / second
- Hard cap (429 above quota, no overage)
- High-volume design-automation throughput
- Bulk transformation arrays per request
- Priority support + uptime SLA
- Unrestricted commercial use in engineering tooling
Built by
Related APIs
Other APIs with overlapping tags.
Pressure Vessel API
Thin-walled pressure-vessel engineering maths as an API, computed locally and deterministically. The thin-wall endpoint computes the wall stresses in a cylindrical or spherical vessel under internal pressure: for a cylinder the hoop (circumferential) stress σ_h = p·r/t and the longitudinal stress σ_l = p·r/(2t), which is half the hoop — so cylinders tend to split along their length — together with the von Mises equivalent stress, and for a sphere the single biaxial stress σ = p·r/(2t); it also reports the radius-to-thickness ratio and whether the thin-wall assumption (r/t ≳ 10) holds. The thickness endpoint computes the wall thickness required to keep the hoop stress within an allowable value, t = p·r/(σ_allow·E), with a weld-joint efficiency factor. The burst endpoint computes the theoretical burst pressure of a pipe from Barlow's formula, p = 2·S·t/OD, using the ultimate tensile strength. Pressures and stresses are in pascals (megapascals also returned) and dimensions in metres. Everything is computed locally and deterministically, so it is instant and private. Ideal for mechanical, chemical-plant, piping, boiler and tank-design app developers, ASME-style sizing and safety tools, and engineering education; for code work consult the applicable standards. Pure local computation — no key, no third-party service, instant. Live, nothing stored. 3 endpoints. This is thin-walled vessel stress; for general stress transformation use a Mohr-circle API and for fatigue a fatigue API.
api.oanor.com/pressurevessel-api
Material Fatigue API
Mechanical-fatigue engineering maths as an API, computed locally and deterministically. The stress-cycle endpoint decomposes a cyclic load given by its maximum and minimum stress into the alternating stress σa = (σmax − σmin)/2, the mean stress σm = (σmax + σmin)/2, the stress range and the stress ratio R = σmin/σmax, and names the loading (fully reversed at R = −1, repeated at R = 0). The criteria endpoint computes the infinite-life safety factor against fatigue using the three classic mean-stress theories — Goodman (1/n = σa/Se + σm/Sut, standard and safe), Soderberg (uses the yield strength, conservative) and Gerber (a parabola, least conservative) — from the alternating and mean stress, the endurance limit Se, the ultimate strength Sut and an optional yield strength. The endurance-limit endpoint estimates the corrected endurance limit Se = ka·kb·kc·kd·ke·Se' from the ultimate strength, with Se' = 0.5·Sut for steel and the Marin modifying factors for surface finish, size, load type, temperature and reliability. Stresses and strengths use any one consistent unit (MPa is typical). Everything is computed locally and deterministically, so it is instant and private. Ideal for mechanical, structural, automotive and aerospace-design app developers, durability and safety-factor tools, and engineering education. Pure local computation — no key, no third-party service, instant. Live, nothing stored. 3 endpoints. This is fatigue and endurance; for static stress transformation use a Mohr-circle API and for column buckling a buckling API.
api.oanor.com/fatigue-api
O-Ring Seal API
O-ring seal-design maths as an API, computed locally and deterministically — the squeeze, gland and stretch numbers an engineer or maker designs a seal to. The squeeze endpoint gives the compression that makes the seal: squeeze = (cross-section − gland depth) ÷ cross-section, so a 0.139-inch cord in a 0.113-inch deep groove is squeezed 18.7 %, and it grades the result — roughly 10–16 % suits dynamic (reciprocating) seals and 15–30 % static ones — and, given the groove width, the gland fill percentage, which should stay under about 85 % so the rubber has room to expand from heat or fluid swell. The gland endpoint works the other way: from the cross-section and whether the seal is static or dynamic (or a target squeeze) it returns the groove depth and a width sized for about 70 % fill — typically 1.3 to 1.5 times the cross-section — plus a corner radius. The stretch endpoint checks installation: stretch = (mating diameter − o-ring ID) ÷ ID, which should stay under about 5 % on a rod because stretching thins the cross-section and steals squeeze. Everything is computed locally and deterministically, so it is instant and private. Ideal for mechanical-engineering, hydraulics, pneumatics, vacuum and product-design app developers, seal-selection and gland-design tools, and CAD plugins. Pure local computation — no key, no third-party service, instant. Inches or millimetres. Live, nothing stored. 3 compute endpoints.
api.oanor.com/oring-api
Gear Ratio API
Gear-train ratio, speed and torque maths as an API, computed locally and deterministically. The ratio endpoint computes the gear ratio of a single pair from the driver and driven tooth counts (or pitch diameters), ratio = N_driven/N_driver, classifies it as a reduction (more torque, less speed) or an overdrive, and — given an input speed and torque — returns the output speed (input/ratio) and the output torque (input·ratio·efficiency). The train endpoint computes a compound gear train: the overall ratio is the product of the individual stage ratios, and it returns each stage ratio, the output speed and torque, noting that idler gears change only the direction of rotation, not the ratio. The solve endpoint finds the missing one of the input speed, the output speed and the ratio from the other two — for example, the ratio needed to drop a 1500 rpm motor to a 500 rpm output. Everything is computed locally and deterministically, so it is instant and private. Ideal for drivetrain, robotics and machine-design tools, gearbox and transmission selection, bicycle and vehicle gearing, and mechanical-engineering education. Pure local computation — no key, no third-party service, instant. Live, nothing stored. 3 endpoints. This is gear-train ratio and torque; for spur-gear tooth geometry use a spur-gear API.
api.oanor.com/gearratio-api
Frequently asked questions
Quick answers about pricing, quotas, and integration.
How do I get an API key for Mohr Circle Stress API?
Sign up for free at oanor.com, generate an API key from the developer dashboard, and call Mohr Circle Stress API with the x-oanor-key header. No credit card needed for the free tier.
What's the rate limit for Mohr Circle Stress API?
Free tier allows 1 request per second. Paid plans scale up to 50 requests per second on the Mega tier. Hard limits return HTTP 429 above the quota — no surprise overage charges.
How much does Mohr Circle Stress API cost?
Mohr Circle Stress API has a free tier with 100 calls / month. Paid plans start at €9.00 / month with higher quotas and faster rate limits.
Can I cancel my subscription anytime?
Yes. Plans are billed monthly and you can cancel anytime from your billing dashboard. No long-term contracts and no cancellation fee.
Is Mohr Circle Stress API GDPR-compliant?
All requests to Mohr Circle Stress API go through our EU-based gateway. Your upstream API key never leaves our server and no personal data is shared with the upstream provider beyond the request you send.
Pick an endpoint from the list on the left to see its details and try it.
Code snippets
Sign up to get an API key, then call any path under your slug.
curl https://api.oanor.com/mohr-api/SOME_PATH \
-H "x-oanor-key: oanor_test_..."const res = await fetch("https://api.oanor.com/mohr-api/SOME_PATH", {
headers: { "x-oanor-key": "oanor_test_..." }
});
const data = await res.json();$ch = curl_init("https://api.oanor.com/mohr-api/SOME_PATH");
curl_setopt($ch, CURLOPT_RETURNTRANSFER, true);
curl_setopt($ch, CURLOPT_HTTPHEADER, ["x-oanor-key: oanor_test_..."]);
$response = curl_exec($ch);import requests
r = requests.get(
"https://api.oanor.com/mohr-api/SOME_PATH",
headers={"x-oanor-key": "oanor_test_..."},
)
print(r.json())Ratings
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