What area and perimeter mean
Area measures the surface a flat shape covers: how many unit squares fit inside it. It is given in square units (cm², m², and so on). Perimeter measures the outline: the total length of the line that goes around the shape, in plain units (cm, m). For a circle, that outline has its own name, the circumference.
These are two of the most useful ideas in school and everyday life: working out how much paint a wall needs (area), how much skirting board to buy for a room (perimeter) or how much fabric covers a table. This calculator solves the five most common shapes instantly, right inside your browser, with nothing sent anywhere.
How to use the calculator
- Choose the shape from the dropdown: square, rectangle, circle, triangle or trapezoid.
- Type the dimensions it asks for. Every value must be a number greater than zero.
- Read the area and perimeter instantly; there is no “calculate” button.
- Press Copy result to drop the summary into your notes.
For a triangle, the area comes from the base and height, while the perimeter needs all three sides. For a trapezoid, the area uses the two bases and the height, and the perimeter also adds the two non-parallel sides. Until you enter them, the perimeter shows a dash.
Formulas by shape
| Shape | Area | Perimeter |
|---|---|---|
| Square | l² | 4·l |
| Rectangle | b·h | 2·(b + h) |
| Circle | π·r² | 2·π·r |
| Triangle | b·h / 2 | a + b + c |
| Trapezoid | (B + b)·h / 2 | B + b + c + d |
Here l is the side, b the base, h the height, r the radius, B and b the trapezoid bases, and a, b, c, d its sides. The value of π (pi) is about 3.14159. Results are rounded to 4 decimal places.
Worked example
Let’s find the area and circumference of a circle with radius 5.
- Area:
π · r² = 3.14159 · 5² = 3.14159 · 25 = 78.5398. - Circumference:
2 · π · r = 2 · 3.14159 · 5 = 31.4159.
Now a rectangle with base 4 and height 6:
- Area:
b · h = 4 · 6 = 24. - Perimeter:
2 · (b + h) = 2 · (4 + 6) = 2 · 10 = 20.
And a trapezoid with longer base 8, shorter base 4, height 5 and sides 6 and 7:
- Area:
(B + b) · h / 2 = (8 + 4) · 5 / 2 = 60 / 2 = 30. - Perimeter:
8 + 4 + 6 + 7 = 25.
Frequently asked questions
What is the difference between area and perimeter?
Area measures what is inside the shape (its surface) and uses square units. Perimeter measures the edge (its outline) and uses plain units. Two shapes can share the same perimeter yet have very different areas, and the other way around.
Why does the circle show “circumference” instead of perimeter?
Because that is the proper name for the outline of a circle. Mathematically it is the same idea: the length that wraps around it, computed with 2·π·r. We use the correct term so it matches your textbooks.
Why does the triangle perimeter ask for all three sides?
Because the base and height are only enough for the area. The height is an internal line perpendicular to the base, not a side of the figure, so it is not part of the outline. The perimeter needs the actual length of all three sides.
Can I use decimals?
Yes. Type values such as 2.5 or 10.75 without any trouble. The calculator accepts decimals with a dot and rounds the result to four figures for readability, while internally it works with your device’s full precision.
What happens if I enter zero or a negative number?
A shape cannot have sides of zero or negative length, so the calculator ignores those values and asks for dimensions greater than zero. Fix the number and the result appears right away.