Area & perimeter formulas
Area is the space inside a flat shape, measured in square units; perimeter is the distance around it, measured in length units. For a rectangle, A = w × h and P = 2(w + h). For a circle, A = πr² and the perimeter (circumference) is C = 2πr.
What each letter means
- w, h
- Width and height (or length and width)
- b, h
- A base and the perpendicular height to it
- r
- Radius: center to edge. Diameter d = 2r
- A, P
- Area (square units) and perimeter (length units)
Area & perimeter formulas calculator
Switch shapes in the menu, or open the area calculator to add and subtract parts of a composite shape.
Give your shape a size.
Use the same unit for every dimension. Changing the unit relabels the measurements; it does not convert them.
From dimensions to an answer
The idea
Area measures a flat region in square units, such as cm². Perimeter measures the length of its boundary, such as cm. For a circle, the perimeter is called the circumference: C = 2πr, while area is A = πr².
Area and perimeter formulas chart
| Shape | Area | Perimeter |
|---|---|---|
| Square (side s) | A = s² | P = 4s |
| Rectangle | A = wh | P = 2(w + h) |
| Triangle | A = ½bh | P = a + b + c |
| Parallelogram | A = bh | P = 2(a + b) |
| Trapezoid | A = ½(a + b)h | Add all four sides |
| Rhombus | A = ½d₁d₂ | P = 4s |
| Circle | A = πr² | C = 2πr = πd |
| Semicircle | A = ½πr² | P = πr + 2r |
| Regular polygon | A = ½ × perimeter × apothem | P = ns |
Worked examples
1Rectangle
- A rectangle is 8 cm by 5 cm.
- Area = 8 × 5 = 40 cm².
- Perimeter = 2(8 + 5) = 26 cm.
Answer: 40 cm² and 26 cm. A 10 cm by 4 cm rectangle also has area 40 cm², but perimeter 28 cm.
2Circle from a diameter
- The diameter is 10 cm, so r = 5 cm.
- Area = π × 5² = 25π ≈ 78.54 cm².
- Circumference = 2π × 5 = 10π ≈ 31.42 cm.
Answer: About 78.54 cm² and 31.42 cm.
3Composite L-shape
- Start with a 10 m by 6 m rectangle and remove a 4 m by 3 m corner.
- Area = 10 × 6 − 4 × 3 = 60 − 12 = 48 m².
- The two cut edges replace the removed edge lengths exactly, so the perimeter stays 2(10 + 6) = 32 m.
Answer: 48 m² and 32 m.
4From perimeter to area (square)
- A square has perimeter 36 cm, so each side is 36 / 4 = 9 cm.
- Area = 9² = 81 cm².
Answer: 81 cm². For a rectangle, perimeter alone does not fix the area: you also need one side.
Common mistakes
- Writing area in plain units. Area is always in square units, such as cm².
- Using a sloping side as the height. The height must be perpendicular to the base.
- Using the diameter in πr². Halve it first.
- Assuming equal perimeters mean equal areas.
Make the formula move.
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Keep exploring
Area & perimeter formulas: common questions
Wondering about the why? Start here.
How do you find the area and perimeter of a shape?
Area uses a formula for the space inside, such as A = wh for a rectangle or A = πr² for a circle. Perimeter adds the lengths around the outside, such as P = 2(w + h). Area is in square units; perimeter is in length units.
Open the area calculatorCan you find the area from the perimeter?
Only for shapes fixed by one length, such as a square (side = P/4) or a circle (r = C/2π). A rectangle with perimeter 20 could be 5 × 5 (area 25) or 9 × 1 (area 9), so you also need one side.
How do you find the area of a composite shape?
Split it into rectangles, triangles, and circle parts. Add the areas of the pieces, and subtract any holes or cut-out corners. The area calculator can add and subtract parts for you.
Calculate a composite area