Geometry Area Converter
Reviewed by Hamza Gujjar, Algorithm Architect & Software Developer
Last updated: August 19, 2026You 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.
Principles of Geometric Area Formulation and Land Surveying Conversions
A geometry area converter computes the two-dimensional surface area for diverse geometric planar polygons and converts area measurements between international metric, US Customary, and historical agricultural land surveying standards. In civil engineering, architectural design, GIS cartography, and real estate valuation, accurate area calculations form the basis for property appraisals and construction material takeoffs.
Universal Geometric 2D Planar Area Formulas
| Geometric Shape | Standard Mathematical Area Formula | Required Input Variables |
|---|---|---|
| Rectangle / Parallelogram | Area = Base (b) × Height (h) | Base length and perpendicular height |
| Triangle (Standard) | Area = 0.5 × Base (b) × Height (h) | Base and perpendicular altitude |
| Triangle (Heron's Formula) | Area = √[ s(s - a)(s - b)(s - c) ] | Three sides a, b, c (s = semi-perimeter = (a+b+c)/2) |
| Trapezoid / Trapezium | Area = [ ( a + b ) / 2 ] × Height (h) | Parallel base lengths a and b, and height |
| Circle | Area = π × r² = ( π × d² ) / 4 | Radius r or Diameter d |
| Ellipse | Area = π × Semi-Major (a) × Semi-Minor (b) | Semi-major axis a and semi-minor axis b |
| Regular Polygon (n sides) | Area = ( n × s² ) / [ 4 × tan(π / n) ] | Number of sides n and side length s |
Land Surveying and Standard Area Unit Conversion Factors
1 Acre = Exactly 43,560 Square Feet = 4,046.8564 Square Meters = 0.404686 Hectares
1 Hectare (ha) = Exactly 10,000 Square Meters = 2.47105 Acres = 107,639 Square Feet
1 Square Kilometer (km²) = 100 Hectares = 247.105 Acres = 0.386102 Square Miles
1 Square Mile (Section) = Exactly 640 Acres = 2.589988 Square Kilometers
Step-by-Step Worked Calculation Example
Example: Calculating Irregular Land Parcel Area and Real Estate Value
Problem: A rural property parcel is surveyed in the shape of a trapezoid with parallel boundary frontages of a = 400.0 feet and b = 650.0 feet, with a perpendicular depth distance h = 320.0 feet. Calculate: (1) Total parcel area in Square Feet; (2) Area converted into Acres and Hectares; and (3) Total land value at an appraised market price of $18,500 per Acre.
Step 1: Calculate trapezoid area in square feet:
Area = [ ( a + b ) / 2 ] × h = [ ( 400.0 + 650.0 ) / 2 ] × 320.0
Area = [ 1,050.0 / 2 ] × 320.0 = 525.0 × 320.0 = 168,000.0 sq ft
Step 2: Convert square feet to Acres (1 Acre = 43,560 sq ft):
Area in Acres = 168,000.0 / 43,560 = 3.8567 Acres
Step 3: Convert Acres to Hectares (1 ha = 2.47105 Acres):
Area in Hectares = 3.8567 / 2.47105 = 1.5608 Hectares (15,608 m²)
Step 4: Calculate total property appraised market value:
Land Value = 3.8567 Acres × $18,500 / Acre = $71,348.95
Conclusion: The 168,000 sq ft property measures 3.86 Acres (1.56 ha) with a market valuation of $71,348.95.
Surveying Coordinates: The Gauss Shoelace Formula
For arbitrary irregular multi-sided land polygons defined by GPS vertices (xi, yi), surveyors compute exact closed boundary area using the Shoelace Formula:
Surface Area of Three-Dimensional Geometric Solids
| 3D Geometric Solid | Total Surface Area Formula | Geometric Parameters |
|---|---|---|
| Sphere | A = 4 × π × r² | Radius r |
| Right Circular Cylinder | A = 2πrh + 2πr² = 2πr(h + r) | Radius r, Height h |
| Right Circular Cone | A = πr√(r² + h²) + πr² | Radius r, Height h |
| Torus (Donut Shape) | A = 4 × π² × R × r | Major radius R, Minor tube radius r |
Historical Land Surveying Units: Chains, Rods, and Perches
In traditional legal deed land descriptions: 1 Gunter's Chain = 66 Feet = 4 Rods = 100 Links. Exactly 10 Square Chains (660 ft × 66 ft) equals 1.0 Acre (43,560 sq ft).