An area calculator finds the surface inside a 2D shape. Pick a shape, type its dimensions, and get the area instantly — in your chosen square units plus automatic conversions to square metres, square feet, acres and hectares. Every result shows the exact formula with your numbers substituted, so you can check the math yourself.
Choose a shape
Formula: A = s² — The area of a square is its side length squared.
Formula: A = l × w — Multiply the two sides together.
Formula: A = πr² — Pi times the radius squared.
Formula: A = ½ × b × h — Half the base times the vertical height.
Formula: A = √[s(s−a)(s−b)(s−c)], s = (a+b+c)/2 — Heron's formula: works from the three side lengths alone.
Formula: A = ½ × (a + b) × h — Half the sum of the two parallel bases times the height.
Formula: A = b × h — Base times the perpendicular height (not the slanted side).
Formula: A = (d₁ × d₂) / 2 — Half the product of the two diagonals.
Formula: A = π × a × b — Pi times the two semi-axes.
Formula: A = (θ/360) × πr² — That fraction of a full circle. Angle must be over 0° and at most 360°.
Unit conversions
Your result in common area units:
How do you calculate the area of a square?
Square the side length: A = s². A square with sides of 5 m has an area of 25 m². Pick the Square tab above and the calculator does this for you, including unit conversion.
Squaring is just multiplying the side by itself, so a 12 ft by 12 ft room is 144 sq ft. If you only know the perimeter, divide it by 4 first to get the side.
What is the formula for the area of a circle?
A = πr²: multiply pi (about 3.14159) by the square of the radius. A circle with radius 2 has area 4π, about 12.566 square units.
If you know the diameter instead, halve it to get the radius first. If you know the circumference C, use A = C² / (4π).
How does Heron's formula work?
From three side lengths a, b and c, compute s = (a + b + c) / 2, then area = √[s(s−a)(s−b)(s−c)]. A 3-4-5 triangle gives s = 6 and area = √(6×3×2×1) = 6.
The sides must satisfy the triangle inequality: each side shorter than the sum of the other two. The calculator rejects impossible sets like 2, 3 and 10 with a clear error message.
How do you convert square feet to square metres?
Multiply square feet by 0.092903 to get square metres. One square metre equals about 10.7639 square feet. So 1,000 sq ft is about 92.9 m².
The conversions panel above does this automatically, along with acres (1 acre = 4,046.86 m²) and hectares (1 hectare = 10,000 m²).
What is the area of a trapezoid?
A = ½(a + b) × h: add the two parallel bases, halve the total, and multiply by the height. Bases of 8 and 12 with height 5 give ½ × 20 × 5 = 50.
The height must be measured perpendicular to the bases, not along the slanted sides. The same caution applies to parallelograms: use the perpendicular height, not the slanted edge length.
Frequently asked questions
What is the formula for the area of a circle?
The area of a circle is pi times the square of the radius: A = pi x r squared. A circle with radius 2 has area 4pi, about 12.566 square units.
How do I find the area of a triangle when I know all three sides?
Use Heron's formula. First find s = (a + b + c) / 2, then area = square root of s(s-a)(s-b)(s-c). A 3-4-5 triangle gives s = 6 and area = 6. The calculator checks the triangle inequality and warns you if the sides cannot form a triangle.
Which units can I convert between?
Input lengths in millimetres, centimetres, metres, kilometres, inches, feet or yards. Results are shown in the matching square unit plus automatic conversions to square metres, square feet, acres and hectares.
What happens if my triangle sides cannot form a triangle?
The calculator shows an error instead of a number. Three lengths form a triangle only when each side is shorter than the sum of the other two (for example 2, 3 and 10 is impossible). Adjust the sides and the result updates.
Is this area calculator really free?
Yes. It is one of 193 free online tools on ZeroFee Tools. There is no signup, no usage limit and no watermark.
Is my data sent anywhere when I use this calculator?
No. All calculations run entirely in your browser with JavaScript. Nothing you type is uploaded or stored.