CalcLibrary

Oval Area Calculator

Measure the long way and the short way of an oval pool, rug, tabletop, or garden bed, then get the enclosed area plus the edging length you need for covers, trim, or border material.

Live formula
Examples

A pool measured 12 ft by 8 ft encloses about 75.40 ft² and needs about 31.73 ft of border length.

Area
75.40 ft²
Approx. perimeter / edging length (Ramanujan)
31.73 ft
Semi-major axis
6.00 ft
Semi-minor axis
4.00 ft

Solved from full long and short measurements first, then converted to the semi-axes with a = major / 2 and b = minor / 2.

Area is exact for an ellipse. Perimeter uses Ramanujan’s approximation, so treat it as a practical planning estimate for edging, trim, or covers rather than a fabrication or surveying guarantee.

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Examples

How It Works

Formula

A=πabA = \pi ab

a=major diameter2a = \frac{\text{major diameter}}{2}

b=minor diameter2b = \frac{\text{minor diameter}}{2}

P≈π(a+b)(1+3h10+4−3h)P \approx \pi(a+b)\left(1 + \frac{3h}{10 + \sqrt{4 - 3h}}\right)

h=(a−ba+b)2h = \left(\frac{a-b}{a+b}\right)^2

Variables

AA

Area enclosed by the oval

PP

Approximate perimeter / edging length

aa

Semi-major axis (center to edge along the long direction)

bb

Semi-minor axis (center to edge along the short direction)

hh

Helper term used in Ramanujan’s perimeter approximation

Choose whether you measured full diameters or already know the semi-axes. In diameter mode, the calculator first converts the long and short dimensions into a = major / 2 and b = minor / 2. It then computes the exact ellipse area with A = piab. For edging length, it uses Ramanujan’s ellipse-perimeter approximation so you can estimate border, trim, or cover-edge material without confusing that estimate with précision fabrication geometry.

Frequently Asked Questions

01What is the difference between long/short diameters and semi-axes?
The long and short diameters are the full end-to-end measurements across the oval. The semi-major axis a and semi-minor axis b are half of those values, measured from the center to the edge. If you enter diameters, the calculator quietly converts them with a = major / 2 and b = minor / 2 before solving the ellipse.
02Is the area exact?
Yes, if your shape is an ellipse. The area formula A = piab is exact for an ellipse, so once the semi-major and semi-minor axes are known, the area is exact geometry.
03Why is the perimeter labeled as approximate?
Unlike the area, ellipse perimeter does not collapse to a simple exact formula in elementary terms. This calculator uses Ramanujan’s well-known approximation, which is practical for planning cover edge, trim, or garden-bed border material without pretending to be fabrication-grade précision.
04What unit should I use?
Any consistent length unit works: meters, centimeters, feet, or inches. Keep both measurements in the same unit. The area result is shown in squared units, while the perimeter stays in the original linear unit.
05When should I use this instead of a circle or rectangle calculator?
Use this when the shape is genuinely oval. Circle formulas assume one radius everywhere, and rectangle formulas assume straight edges with square corners. If you are measuring an oval pool, rug, tabletop, or planting outline, ellipse math is the closer match.

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