Arc Radius from Chord & Rise Calculator
Find the radius and curved length of a shallow circular arch from its span and rise.
Set up your calculation
An illustrative example is loaded. Replace its values with your measurements, costs or documented settings.
Calculation
Your result
- Radius
- 500 mm
- Included arc angle
- 73.74 °
- Curved arc length
- 643.501 mm
The quote handoff carries your inputs and assumptions. Only an explicit base cost is suggested as a quote cost; prices, rates and measurements remain planning notes.
Method & assumptions
Radius = chord² ÷ (8 × rise) + rise ÷ 2. Included angle = 2 × asin(chord ÷ (2 × radius)); arc length = radius × angle in radians.
- Models a minor circular arc with rise no greater than half the chord. Not an ellipse, catenary or multi-center arch.
- Dimensions describe a reference curve, not stock thickness, bending allowance or springback.
Work through the arc radius example
| Input or step | Example value |
|---|---|
| Example inputs | 600 mm span and 100 mm rise |
| Radius | 500 mm |
| Included arc angle | 73.739795 ° |
| Curved arc length | 643.501109 mm |
These values match Load example. They illustrate the method, not recommended material, machine or pricing settings. Read the assumptions before using the result.
Common questions
Are the example settings a recommendation?
No. Replace the example with measured dimensions, actual costs and your product or machine manufacturer's limits.
What if an input is incomplete or impossible?
The result is hidden and a field or calculation error explains what needs correction.
Use this in your project
Continue with the next measurement or cost, then keep the assumptions with your quote.
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