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Accurately calculate the area of an ellipse by entering the semi-major and semi-minor axes. Supports customizable units and decimal precision.
Overview
Understand what the tool solves, how it works, and the boundaries of its data.
An ellipse area calculator needs the distance from the center to the edge along each of the two perpendicular axes. The longer half-distance is the semi-major axis, a; the shorter is the semi-minor axis, b. If your drawing gives the full end-to-end length and width, divide each by two before entering them. For example, full dimensions of 10 cm by 6 cm mean a = 5 cm and b = 3 cm.
Area: A = πab
With the example above, A = π × 5 × 3 = 15π ≈ 47.1239. Because both inputs are lengths, the area is in square units: square centimeters in this example. If both values are entered in inches, read the result as square inches. The calculator has no unit selector or automatic unit conversion.
The area relation follows by scaling a circle in one direction: the two semi-axes set the ellipse's horizontal and vertical scale. If the axes are equal, the shape is a circle and the formula becomes πr².
The page also displays an approximate perimeter using a Ramanujan formula. It is a separate result from the area, which uses the direct ellipse area formula.
Perimeter ≈ π[3(a + b) − √((3a + b)(a + 3b))]
For a = 5 and b = 3, the calculator returns an area of 47.1239 and an estimated perimeter of 25.5270. The first is expressed in square units; the second uses the same length unit as the inputs. The perimeter is explicitly approximate, so do not treat its four displayed decimal places as a claim of exactness.
A = πab and axis terminology; checked 2026-09-28.Guide
Follow the workflow and verify inputs and outputs with practical examples.
Measure or read the full major and minor diameters. Divide each by two to get the center-to-edge values required by the inputs. Put the larger half-axis in the semi-major field for clear records.
Convert first if one measurement is in feet and the other is in inches. The calculator multiplies the entered numbers as-is; it does not identify unit labels or reconcile different scales.
Positive numeric values produce an area and an estimated perimeter, displayed to four decimal places. Attach the squared unit to the area and the unsquared unit to the perimeter when recording or sharing the values.
As a quick check, entering 10 and 10 gives the area of a radius-10 circle, approximately 314.1593, and a perimeter of approximately 62.8319. Swapping two valid axis values leaves these formulas' results unchanged, although labeling the larger one a follows standard notation.
Use cases
See how the tool fits into real work and everyday tasks.
When a problem gives semi-axes, enter them directly and compare the area against πab. When it gives full axis lengths, halve both first; this catches the common factor-of-four area error.
For a clearly elliptical opening, panel, or tabletop with known major and minor dimensions, calculate its modeled face area. Keep the dimensions and unit beside the result so another person can reproduce it.
Designers can compare modeled ellipse areas before choosing a size. Use the perimeter estimate only when an approximate edge length is useful, such as an early trim estimate.
Q&A
Find concise answers to common questions and confusing cases.
Not directly. The inputs represent half-axes measured from the center. Divide each full end-to-end dimension by two first.
No. Enter both axis values in the same unit. The output unit follows from those values: squared for area and unchanged for perimeter.
The page uses a Ramanujan approximation for the ellipse boundary. Its displayed value is an estimate, unlike the area calculated from πab.
Notes
Review scope, result limitations, and important precautions before use.
The calculation models a flat, standard ellipse using two perpendicular semi-axes. If an outline is irregular, tilted in a way that changes the measured projection, or not centered on the dimensions you measured, this model may not describe its actual area. Four decimal places are display rounding; they do not add precision to approximate measurements. For fabrication tolerances or other precision-critical work, use the method and tolerances specified for that project.
Keep both inputs in the same unit. A mixed-unit pair can produce a plausible-looking number with the wrong scale, because unit text is not parsed or converted.
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