DIY Cost Tools
Ellipse Area Calculator
MATH & GEOMETRY CALCULATOR
Find ellipse area and estimate perimeter from its two semi-axes.
Use the same length unit throughout. All fields are required. Perimeter is an approximation, especially for elongated ellipses. Inputs describe a flat ideal ellipse.
How to use this calculator
Enter your dimensions and select Calculate. Length results use your input unit, areas use its square, and volumes use its cube. Retain measurement precision until the final answer.
Formula and explanation
Area = πab; approximate perimeter = π[3(a+b) − √((3a+b)(a+3b))]
Semi-axes are half the full width and height. Area is exact for an ideal ellipse; perimeter uses the first Ramanujan approximation.
Worked example
For Semi-major axis (units) = 5, Semi-minor axis (units) = 3, results are Area (square units): 47.12389; Approximate perimeter (units): 25.526986.
Important limitations
Perimeter is an approximation, especially for elongated ellipses. Inputs describe a flat ideal ellipse.
Ideal geometry does not account for manufacturing tolerances or measurement uncertainty. This is a calculation aid, not a structural design or building-code approval. Absolute inputs must not exceed one trillion.
Frequently asked questions
What is a semi-axis?
The center-to-boundary distance along a principal axis.
Can I use full width and height?
Divide each by two first.
Can I mix inches and centimeters?
Convert all lengths to one unit first. Mixed units produce incorrect results.
Why did my result disappear?
Blank, invalid, or out-of-range inputs clear the previous result and display an instruction.
Review notes
Reviewed October 1, 2026. Default results were checked against the displayed formulas. Script tests covered blank, negative, nonfinite, and excessive inputs. Results run locally in your browser.