Ellipse Area Calculator

Area is simply π times both semi-axes, but the perimeter has no closed elementary form — this uses Ramanujan’s approximation.

Your numbers

Semi-major axis(cm)Semi-minor axis(cm)

Area

188.5cm²

Circumference

51.05cm

Formula

Area = π × Semi-major axis × Semi-minor axis

Equal semi-axes give a circle. Entering diameters instead of semi-axes quadruples the area.

What to enter

Input	Default	Accepted range
Semi-major axis (cm)The longer radius of an ellipse.	10	0 and up
Semi-minor axis (cm)The shorter radius of an ellipse.	6	0 and up

Step by step

FormulaArea = π × Semi-major axis × Semi-minor axis

With the default numbersArea = π × 10 × 6

AnswerArea = 188.5 cm²

Quick reference table

Results when only Semi-major axis (cm) changes and everything else stays put.

Semi-major axis (cm)	Area (cm²)	Circumference (cm)
5	94.25	34.63
7.5	141.37	42.54
10	188.5	51.05
15	282.74	69.04
20	376.99	87.72

What each result means

Result	At default values
Area (cm²)The space a shape covers — length squared.	188.5
Circumference (cm)The distance once around a circle.	51.05

Common mistakes

Equal semi-axes give a circle. Entering diameters instead of semi-axes quadruples the area.

Glossary

Semi-major axis: The longer radius of an ellipse.
Semi-minor axis: The shorter radius of an ellipse.
Area: The space a shape covers — length squared.
Circumference: The distance once around a circle.

Frequently asked questions

QHow is Ellipse Area Calculator calculated?

Area = π × Semi-major axis × Semi-minor axis — Area is simply π times both semi-axes, but the perimeter has no closed elementary form — this uses Ramanujan’s approximation.

QCan you walk through an example?

With Semi-major axis 10cm, Semi-minor axis 6cm, the answer is Area 188.5cm².

QWhat do I need to enter?

Enter Semi-major axis, Semi-minor axis. The result recalculates as you type, and an empty box counts as zero.

QHow much does the answer move if I change a number?

Changing only Semi-major axis (cm) moves the answer to Semi-major axis (cm) 5 → Area (cm²) 94.25 and Semi-major axis (cm) 20 → Area (cm²) 376.99. The table below lays out five steps.

QHow are the numbers rounded?

Money is shown to the nearest whole unit, percentages to one decimal place and everything else to two. What you see is rounded; the calculation itself carries the unrounded value forward.

QAnything to watch out for?

Equal semi-axes give a circle. Entering diameters instead of semi-axes quadruples the area.

Related calculators

Circle Area CalculatorGet the area and circumference of a circle from its radius.Radius from CircumferenceMeasure around an object and work back to radius and area.Triangle Area CalculatorFind a triangle’s area from its base and height.Heron's Formula CalculatorFind a triangle’s area from three side lengths, without knowing the height.

Keep your length units consistent across inputs — mixing centimetres and metres throws results far off.