Area Calculator
Calculate and convert the area of rectangles, triangles, circles, trapezoids, parallelograms, and ellipses.
Content updated August 4, 2026
Every entered length must use the selected input unit. Triangle, trapezoid, and parallelogram inputs do not contain enough side information to determine a full perimeter. Ellipse circumference is a Ramanujan approximation; area is calculated directly.
Calculate the area of a rectangle, triangle, circle, trapezoid, parallelogram, or ellipse from the measurements that uniquely determine that area. Every entered length uses one input unit, and the completed area can be converted to a different squared metric or imperial unit.
The calculator keeps length and area dimensions separate: converting a length by a factor of k converts its area by k². It also shows the equivalent square side and, where the entered dimensions determine it, a boundary length.
The Area formula
Rectangle: A = lw · Triangle: A = bh/2 · Circle: A = πr² · Trapezoid: A = (a+b)h/2 · Parallelogram: A = bh · Ellipse: A = πabAll lengths share one input unit · h is perpendicular height · r is radius · ellipse a and b are semi-axes · area conversion uses the square of the length factor.
Worked example
A rectangle 12 m long and 8 m wide has area 12 × 8 = 96 m² and perimeter 2(12+8) = 40 m. Converting the area to square centimetres multiplies by 100², giving 960,000 cm².
Assumptions, rounding, and limitations
Assumptions
- The selected shape is a plane Euclidean figure and every entered length uses the selected input unit.
- Triangle, trapezoid, and parallelogram heights are perpendicular to their stated bases.
- Circle input is a radius; ellipse inputs are semi-axes measured from the center.
- Input measurements are treated as exact at the precision entered.
Rounding: The engine retains floating-point precision through the formula and squared unit conversion. Displays show up to eight decimal places; ellipse boundary uses Ramanujan's approximation before display rounding.
Limitations
- Each dimension must be greater than zero and no more than 1 billion; supported length units are mm, cm, m, in, ft, and yd.
- Does not handle composite, irregular, coordinate-defined, curved-surface, spherical, or self-intersecting regions, holes, waste factors, or measurement uncertainty.
- The boundary is unavailable when the chosen area inputs do not uniquely determine every side, and ellipse circumference is approximate.
Sources
- SI Units — Area — National Institute of Standards and Technology
- NIST Guide to the SI, Appendix B.9: Conversion Factors — National Institute of Standards and Technology
Selecting the right measurements
A rectangle uses length and width. A triangle and parallelogram use a base and its perpendicular height. A trapezoid uses its two parallel bases and perpendicular height. A circle uses radius, while an ellipse uses its two semi-axes measured from the center.
Base-and-height inputs do not determine every side of a general triangle, trapezoid, or parallelogram, so this tool does not invent a perimeter for those shapes. Rectangle and circle boundaries are exact from the entered values; ellipse circumference uses Ramanujan's well-known approximation.
Why square-unit conversion uses a squared factor
Area has two length dimensions. Since one metre equals 100 centimetres, one square metre is 100 × 100 = 10,000 square centimetres, not 100 square centimetres.
NIST identifies the square metre as the SI derived unit of area and publishes conversion factors for square feet, square inches, and square yards. This calculator first solves the shape in the input unit, then applies the square of the exact length factor.
Frequently asked questions
▶Which height should I use for a triangle?
Use the perpendicular distance from the selected base to the opposite vertex, not a sloping side unless that side is perpendicular to the base.
▶How do I calculate a circle's area?
Enter the radius, which is the distance from the center to the edge. The calculator applies A = πr².
▶Why does one square metre equal 10,000 square centimetres?
Each of the area's two dimensions changes by 100, so the combined factor is 100² = 10,000.
▶Does the triangle result include its perimeter?
No. A base and perpendicular height determine area but do not uniquely determine the other two side lengths.
▶Is ellipse circumference exact?
The ellipse area is calculated directly as πab. The displayed boundary uses Ramanujan's approximation and is explicitly labeled approximate.
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Open calculator →Disclaimer: Area Calculator results are estimates for general information and education only, and are not financial, tax, legal or medical advice. Verify important decisions with a qualified professional.