Ellipse Area & Perimeter Calculator
Ellipse Area & Perimeter Calculator
An ellipse is a stretched circle, defined by two radii: the semi-major axis (the longer one) and the semi-minor axis (the shorter one). Enter both, and this calculator finds the area and the perimeter, along with a diagram and the full step-by-step working.
The area formula is exact and elegant — simply π times the two semi-axes multiplied together — but an ellipse's perimeter has no equally simple exact formula, unlike a circle's circumference; this calculator instead uses Ramanujan's second approximation, a well-known formula that stays accurate to within a tiny fraction of a percent for virtually any realistic ellipse shape. This asymmetry between a clean area formula and an approximated perimeter formula is a genuinely interesting quirk of ellipse geometry that surprises people who assume every shape's measurements have equally tidy exact formulas.
- Area = πab, an exact formula - so semi-axes of 6 and 4 give an area of π × 6 × 4 ≈ 75.40 square units.
- Unlike the area, there's no simple exact formula for an ellipse's perimeter - this calculator uses Ramanujan's second approximation, which is accurate to within a tiny fraction of a percent for virtually any ellipse shape.
- When a = b, an ellipse becomes a circle, and both formulas simplify to the familiar circle formulas (πr² and 2πr).
How do I find the area of an ellipse?
Use Area = πab, where a and b are the two semi-axes. For semi-axes 6 and 4: π × 6 × 4 ≈ 75.40.
Why is the ellipse perimeter only an approximation?
The exact perimeter requires an elliptic integral that can't be written with elementary functions - Ramanujan's approximation formula gets extremely close (typically well under 0.05% error) without needing calculus.
Ellipse Area & Perimeter Calculator
An ellipse is a stretched circle, defined by two radii: the semi-major axis (the longer one) and the semi-minor axis (the shorter one). Enter both, and this calculator finds the area and the perimeter, along with a diagram and the full step-by-step working.
The area formula is exact and elegant — simply π times the two semi-axes multiplied together — but an ellipse's perimeter has no equally simple exact formula, unlike a circle's circumference; this calculator instead uses Ramanujan's second approximation, a well-known formula that stays accurate to within a tiny fraction of a percent for virtually any realistic ellipse shape. This asymmetry between a clean area formula and an approximated perimeter formula is a genuinely interesting quirk of ellipse geometry that surprises people who assume every shape's measurements have equally tidy exact formulas.
- Area = πab, an exact formula - so semi-axes of 6 and 4 give an area of π × 6 × 4 ≈ 75.40 square units.
- Unlike the area, there's no simple exact formula for an ellipse's perimeter - this calculator uses Ramanujan's second approximation, which is accurate to within a tiny fraction of a percent for virtually any ellipse shape.
- When a = b, an ellipse becomes a circle, and both formulas simplify to the familiar circle formulas (πr² and 2πr).
How do I find the area of an ellipse?
Use Area = πab, where a and b are the two semi-axes. For semi-axes 6 and 4: π × 6 × 4 ≈ 75.40.
Why is the ellipse perimeter only an approximation?
The exact perimeter requires an elliptic integral that can't be written with elementary functions - Ramanujan's approximation formula gets extremely close (typically well under 0.05% error) without needing calculus.