# Area Calculator

> Area is length × width for a rectangle, π × r^2 for a circle and base × height ÷ 2 for a triangle, so a 12 × 10 ft room is 120 sq ft and a circle with a 5 ft radius is about 78.54 sq ft. Pick a shape to see the formula and working, plus metric and acre conversions.

- Interactive calculator: https://calculatorswithsteps.com/area-calculator
- Category: Math & Statistics Calculators
- Last updated: 2026-11-10
- Publisher: Calculators With Steps (calculatorswithsteps.com)

## How to use the area calculator

1. Choose the **shape** from the list. There are 12 options, including two ways to measure a triangle and a circle.
2. Choose the **length unit** you measured in: mm, cm, m, km, inches, feet, yards or miles.
3. Enter the measurements. Keep every length in the same unit.

You get the area in that unit squared (ft², m² and so on), the formula, the working, the perimeter where it can be found, and a table converting the area to every common unit, including acres and hectares.

## Area formulas for common shapes

| Shape | Area formula | Example | Area |
| --- | --- | --- | --- |
| Square | A = s² | s = 10 | 100 |
| Rectangle | A = length × width | 12 × 10 | 120 |
| Triangle | A = ½ × base × height | b = 10, h = 6 | 30 |
| Triangle (3 sides) | A = √(s(s − a)(s − b)(s − c)) | 13, 14, 15 | 84 |
| Circle | A = πr² | r = 5 | 78.5398 |
| Ellipse | A = πab | a = 6, b = 4 | 75.3982 |
| Trapezoid | A = ½(a + b)h | 8, 12, h = 5 | 50 |
| Parallelogram | A = base × height | 10 × 6 | 60 |
| Rhombus | A = (p × q) ÷ 2 | diagonals 8 and 6 | 24 |
| Sector | A = (θ ÷ 360°) × πr² | r = 10, θ = 60° | 52.3599 |
| Regular polygon | A = ns² ÷ (4 tan(180° ÷ n)) | hexagon, s = 4 | 41.5692 |

In Heron's formula, s is the semi-perimeter, (a + b + c) ÷ 2. For the 13-14-15 triangle, s = 21 and the area is √(21 × 8 × 7 × 6) = √7,056 = 84.

The height of a triangle, parallelogram or trapezoid is always measured at right angles to the base, not along a slanted side. If you only know a slanted side and part of the base, the [Pythagorean theorem calculator](https://calculatorswithsteps.com/pythagorean-theorem-calculator) can find the height.

## Worked examples

**A bedroom floor.** A room measures 12 ft by 10 ft. Area = 12 × 10 = **120 ft²**, which is about **11.1484 m²**. The perimeter, useful for skirting boards, is 2 × (12 + 10) = 44 ft.

**A round patio.** A circular patio has a radius of 5 m. Area = π × 5² ≈ **78.5398 m²**, or about 845.3955 square feet, and the circumference is about 31.4159 m.

**A building plot.** A rectangular lot is 100 ft by 200 ft. Area = **20,000 ft²**, which is about 1,858.0608 m², **0.459137 acres** or 0.185806 hectares.

**A hexagonal table top.** A regular hexagon with 4 m sides has an area of about 41.5692 m² and a perimeter of 24 m.

## Converting square units

Squaring the unit squares the conversion factor too. One foot is 0.3048 m, but one square foot is 0.3048² = 0.09290304 m², not 0.3048 m².

| Unit | In square metres |
| --- | --- |
| 1 square inch | 0.00064516 m² |
| 1 square foot | 0.09290304 m² |
| 1 square yard | 0.83612736 m² |
| 1 acre (43,560 ft²) | 4,046.8564224 m² |
| 1 hectare | 10,000 m² |
| 1 square mile (640 acres) | 2,589,988.110336 m² |

These factors follow the international yard and pound definitions used by NIST, where 1 inch is exactly 2.54 cm. Convert any lengths to a single unit before you start, because mixing feet and inches is the most common source of wrong answers.

## Irregular shapes and practical tips

- **Split complex shapes.** An L-shaped room is two rectangles. A room with a bay window is a rectangle plus a trapezoid. Work out each part and add them.
- **Subtract cut-outs.** For a lawn with a round flower bed, find the rectangle's area and subtract the circle.
- **Buy a little extra.** Flooring, tiles and turf are usually bought with 5 to 10% extra for cutting and waste. The [square footage calculator](https://calculatorswithsteps.com/square-footage-calculator) adds that allowance and works out cost.
- **Need depth as well?** If you are pouring a slab or filling a bed, area alone is not enough. Use the [volume calculator](https://calculatorswithsteps.com/volume-calculator) or the [concrete calculator](https://calculatorswithsteps.com/concrete-calculator).
- **Measure twice.** A 1-inch error on each side of a 12 × 10 ft room changes the area by almost 2 square feet.

## Frequently asked questions

### How do you calculate area in square feet?

Measure the length and width in feet and multiply them. A room 12 ft long and 10 ft wide is 12 × 10 = 120 square feet. If you measured in inches, multiply and then divide by 144, because one square foot is 144 square inches.

### How do you calculate the area of a circle?

Use A = πr², where r is the radius. A circle with a radius of 5 m has an area of π × 25 ≈ 78.5398 m². If you know the diameter, halve it first: a 10 m diameter gives the same 5 m radius.

### How do you find the area of a triangle?

With the base and the perpendicular height, A = ½ × base × height, so a base of 10 and a height of 6 give 30. With only the three sides, use Heron's formula: sides 13, 14 and 15 give an area of 84.

### How do I calculate the area of a trapezoid?

Average the two parallel sides and multiply by the height: A = ½ × (a + b) × h. With parallel sides of 8 and 12 and a height of 5, the area is 10 × 5 = 50.

### How many square feet are in an acre?

One acre is exactly 43,560 square feet, or about 4,046.86 m². A 100 ft × 200 ft lot is 20,000 square feet, which is about 0.459137 acres or 0.185806 hectares.

### How do I find the area of an irregular shape?

Split it into rectangles, triangles and circles, find each area and add them. An L-shaped room made of a 12 × 10 ft section and a 6 × 4 ft section has an area of 120 + 24 = 144 square feet.

### How do you convert square metres to square feet?

Multiply by about 10.7639, because one foot is exactly 0.3048 m and one square foot is 0.09290304 m². For example, 50 m² is about 538.1955 square feet.

### What is the difference between area and perimeter?

Area measures the surface inside a shape in square units. Perimeter measures the distance around it in ordinary units. A 12 × 10 ft room has an area of 120 square feet and a perimeter of 44 feet.

## Sources

- [Wikipedia – Area](https://en.wikipedia.org/wiki/Area)
- [Wolfram MathWorld – Heron's Formula](https://mathworld.wolfram.com/HeronsFormula.html)
- [NIST – Unit conversion (SI and US customary units)](https://www.nist.gov/pml/owm/metric-si/unit-conversion)