Perimeter of an Ellipse Calculator
Calculates the perimeter of an ellipse from the measurements you enter. Use any unit, as long as all inputs use the same one.
Result
- Perimeter (Ramanujan)
- 31.7309
How to use the perimeter of an ellipse calculator
- Enter the semi-major axis.
- Enter the semi-minor axis.
- The results update as you type, or press Calculate.
- Read the perimeter (ramanujan) first, then the supporting figures below it.
Formula
π[3(a+b) − √((3a+b)(a+3b))]
Worked example
For example, with these inputs:
- Semi-major axis: 6
- Semi-minor axis: 4
the calculator returns:
- Perimeter (Ramanujan): 31.7309
Background
Calculators are best used to check working rather than replace it, especially for exams where method marks count. Work the problem by hand first, then confirm with the calculator.
A quick mental estimate before calculating is a powerful check. If a room's floor area comes out at 4,000 square metres or a percentage comes out above 100% when it should not, you know to look again.
Frequently asked questions
How does the perimeter of an ellipse calculator work?
It applies this formula: π[3(a+b) − √((3a+b)(a+3b))]
Can I use any units?
Yes, as long as every input uses the same unit. The answer will be in that unit (squared for areas, cubed for volumes).