Ellipse Circumference Calculator
Estimate ellipse perimeter from its two semiaxes using Ramanujan’s second approximation.
Formula
h=((a−b)/(a+b))²; P ≈ π(a+b)[1+3h/(10+√(4−3h))].
First semiaxis: 5 cm · Second semiaxis: 3 cm · Approximate perimeter ≈ pi×((5 cm × 0.01 m/cm)+(3 cm × 0.01 m/cm))×(1+3×(0.0625)÷(10+sqrt(4-3×(0.0625))))×100
How to use
- Enter both semiaxes, not full axes.
- Choose each length unit.
- Read the approximate perimeter in cm.
Examples
- Semiaxes 5 cm and 3 cm give about 25.526999 cm.
Frequently asked questions
Is circumference the same as perimeter?
Yes. Both mean the length around the ellipse.
Is the result exact?
Only in the circle case. This uses Ramanujan II without the extra correction term in the NIST discussion.
Must a be larger?
No. The formula is symmetric. Both lengths must be positive.
Sources
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