Geometry Area Converter
You Solved the Geometry. Now the Units Have to Match.
Most area problems arrive in two stages. First you compute the area from a shape formula — base times height, πr², half the product of the diagonals. Then you discover the answer is in the wrong unit: you measured a circle's radius in inches and the answer needs to be in square feet, or a plot's dimensions in metres and the answer needs to be in acres. This converter handles the second stage, and it handles it with squared factors, which is where hand conversion usually goes wrong.
The Formula
(Factors are relative to 1 square meter)
Every factor is the corresponding linear factor raised to the second power. That single fact explains all the counter-intuitive results: because 1 ft = 0.3048 m, 1 ft² = 0.09290304 m² — and 1 m² is therefore 10.76391042 ft², not 3.28. Negative values are rejected; a shape cannot enclose negative area.
The Shape Formulas That Feed This Converter
Compute the area first, then convert. The standard planar formulas:
| Shape | Area formula | Result unit |
|---|---|---|
| Square | s² | square of input unit |
| Rectangle | length × width | square of input unit |
| Triangle | ½ × base × height | square of input unit |
| Circle | π × r² | square of input unit |
| Parallelogram | base × height | square of input unit |
| Trapezoid | ½ × (a + b) × height | square of input unit |
| Ellipse | π × a × b | square of input unit |
Squaring Changes the Factor
A square metre holds 10.76 square feet, not 3.28 — the linear factor squares when the dimension does.
Complete Factor Reference
| Unit | Code | Square Meters | Square Feet |
|---|---|---|---|
| Square Millimeters | mm2 | 0.000001 | 0.00001076 |
| Square Centimeters | cm2 | 0.0001 | 0.00107639 |
| Square Meters | m2 | 1 | 10.76391042 |
| Hectares | hectare | 10000 | 107639.1042 |
| Square Kilometers | km2 | 1000000 | 10763910.4167 |
| Square Inches | in2 | 0.00064516 | 0.00694444 |
| Square Feet | ft2 | 0.09290304 | 1 |
| Square Yards | yd2 | 0.83612736 | 9 |
| Acres | acre | 4046.8564224 | 43560 |
| Square Miles | mi2 | 2589988.110336 | 27878400 |
1 in² = 0.00694444 ft² is exactly 1/144 — there are 144 square inches in a square foot, because there are 12² of them.
Problems This Solves
- Geometry homework with mixed units — a question that gives dimensions in centimetres but asks for the answer in square metres. Solve in cm², convert once at the end.
- CAD and drafting — a model built in millimetres reporting a face area that has to be quoted in square inches for a supplier.
- Surveying irregular plots — splitting a plot into triangles, summing the areas in square metres, then reporting the total in acres or hectares.
- Cross-sectional area — a pipe's πr² computed from a radius in inches, needed in square millimetres for a flow calculation.
How to Use This Calculator
- Work out the area using the appropriate shape formula, keeping the unit you measured in.
- Enter that number in the Value field.
- Set the first dropdown to the squared unit you computed in — square centimetres if you measured in centimetres, and so on.
- Set the second dropdown to the unit the answer needs to be in.
- Press Calculate. Both factors and the division are shown alongside the result.
Related Calculations
For land, property and floor-area work specifically, the Area Converter covers the same units with parcel-oriented reference tables. Converting the underlying dimensions instead? Use the Length Converter.