Ellipse Circumference Calculator
Enter the full width and full height through the centre of an ellipse. The form opens with a 10 cm by 6 cm example and shows an approximate circumference. Use decimal lengths in one unit; changing the unit changes its label without converting the numbers.
Ellipse / oval circumference
Enter the full width and full height through the centre, in the same unit. This form treats the oval as an ellipse.
Full axes: 10 cm × 6 cm. Semiaxes: 5 cm and 3 cm.
Ellipse circumference uses Ramanujan’s second approximation, not an exact pi expression. Enter both full axis lengths in the same unit; the calculation halves them to semiaxes. Approximation error grows as the ellipse becomes more elongated. Decimal places control display rounding, not approximation accuracy.
Formula: C ≈ π(a + b)(1 + 3h / (10 + √(4 − 3h))), where h = ((a − b) / (a + b))² and a, b are semiaxes. Formula reference.
Common questions
- Should I enter full axes or semiaxes?
- Enter full axis lengths: the complete width and complete height through the centre. The form halves them to a and b, the semiaxes used in the formula. A 10 cm by 6 cm ellipse has semiaxes 5 cm and 3 cm and an approximate circumference of 25.527 cm to four decimal places.
- Is an ellipse circumference the same as a circle circumference?
- Only when the two axes are equal. A 6 cm by 6 cm ellipse is a circle with radius 3 cm, so its circumference is 6π cm, about 18.8496 cm. For unequal axes this form uses an approximation; the circle calculator supplies exact pi expressions for circles.
- How accurate is the approximation?
- The form uses Ramanujan’s second approximation, C ≈ π(a + b)(1 + 3h / (10 + √(4 − 3h))), with h = ((a − b) / (a + b))². It is especially close for ellipses near circular and becomes less accurate for very elongated ellipses. Adding displayed decimal places does not remove approximation error.
- Can I use this for any oval?
- This form assumes a mathematical ellipse. A stadium shape made from two straight sides and two semicircles, or an irregular oval, can have a different perimeter with the same width and height. Measure or use the formula for that shape instead.
Ellipse circumference uses Ramanujan’s second approximation, not an exact pi expression. Enter both full axis lengths in the same unit; the calculation halves them to semiaxes. Approximation error grows as the ellipse becomes more elongated. Decimal places control display rounding, not approximation accuracy.