Geometry Calculator
Pick a shape, enter its dimensions and get the area, the perimeter or circumference and related measures such as diagonal, apothem or median. Triangles work from a base and height or from three sides. For three-dimensional solids, use the volume calculator.
Last updated November 4, 2026
Result
Area = 78.5398, circumference = 31.4159
| Measure | Value |
|---|---|
| Area | 78.5398 square units |
| Circumference | 31.4159 |
| Diameter | 10 |
Use one unit for every length. Areas are in that unit squared. Results are rounded to 4 decimal places.
Show the work
Formula: area = pi x r²; circumference = 2 x pi x r
- Radius r = 5.
- Area = pi x 5² = pi x 25 = 78.5398.
- Circumference = 2 x pi x 5 = 31.4159.
- Diameter = 2 x 5 = 10.
Result: Area = 78.5398, circumference = 31.4159
Area and perimeter formulas
circle: A = πr² · rectangle: A = l × w · triangle: A = b × h / 2 · trapezoid: A = (a + b) × h / 2
A circle of radius r has area πr² and circumference 2πr. A rectangle has area length times width and perimeter 2(l + w), with a diagonal of √(l² + w²). A parallelogram has area base times perpendicular height, and the height is not the slanted side. A trapezoid has area equal to the average of its two parallel sides times the height.
A regular polygon with n equal sides of length s has perimeter n × s, apothem s / (2 tan(180°/n)) and area n × s × apothem / 2. An ellipse with semi-axes a and b has area πab. Its perimeter has no exact closed form, so this calculator uses Ramanujan’s second approximation, which is very accurate for the shapes you are likely to meet.
See how we calculate for the formulas, sources and review schedule behind every calculator.
Also useful alongside this calculator: Square Footage Calculator, Length Converter and Circumference Calculator.
Triangles from a base and height or three sides
If you know a base and the perpendicular height to it, the area is half their product. If you know only the three sides, the calculator applies Heron’s formula for you, and the area calculator shows that formula step by step with a worked example.
Three lengths form a triangle only when each is shorter than the sum of the other two. Sides of 1, 2 and 3 fail because 1 + 2 equals 3, so the calculator reports that no triangle exists instead of returning an area of zero.
Geometry calculator or area calculator?
Use this geometry calculator when you want the whole picture of a common shape: area together with the perimeter or circumference, plus measures such as the diagonal, apothem or median. It suits homework and any job needing more than one measurement.
Switch to the area calculator when area is the only answer you need. It adds sectors, Heron’s formula shown in full, and the result converted into six square units at once.
Units and squared units
The calculator does not need to know your unit. Enter every length in the same one and read the result in that unit. Lengths stay in the unit, while areas are in square units: centimeters give square centimeters and feet give square feet.
Never mix units in one calculation. A rectangle 2 m by 50 cm is 2 × 0.5 = 1 square meter, not 100. Convert first with the length converter if needed.
Regular polygons
Regular means all sides and all angles are equal. Each interior angle is (n - 2) × 180° / n, so a square has 90°, a regular pentagon 108° and a hexagon 120°. The circumradius is the distance from the center to a corner, and the apothem is the distance from the center to the middle of a side.
A hexagon of side 2 has circumradius exactly 2, because it splits into six equilateral triangles. Its area is 6 × (√3/4) × 2² ≈ 10.3923.
Volume and other solids
This page covers flat shapes. Boxes, cylinders, cones and spheres have volume and surface area, which are separate formulas. Use the volume calculator for those.
The calculator rejects zero and negative lengths, because a shape with no size has no area worth reporting.
How to use the Geometry Calculator
- Choose the shape from the list, using the base-and-height or three-sides option for triangles.
- Enter each dimension as a number greater than zero, all in the same unit.
- Read the area, perimeter and related measures in the results table.
- Open Show the work to check each formula, then Copy or Share the result.
Worked example
A garden bed is a trapezoid with parallel sides of 6 m and 10 m and a height of 4 m. Its area is (6 + 10) / 2 × 4 = 32 square meters. If the slanted legs are 5 m each, the perimeter is 6 + 10 + 5 + 5 = 26 m. A circular pond of radius 5 m covers π × 5² ≈ 78.5398 square meters and has a circumference of about 31.4159 m. The table lists more shapes.
| Shape | Dimensions | Area | Perimeter |
|---|---|---|---|
| Circle | r = 5 | 78.5398 | 31.4159 |
| Rectangle | 8 × 5 | 40 | 26 |
| Triangle | 13, 14, 15 | 84 | 42 |
| Trapezoid | 6, 10, h = 4, legs 5 | 32 | 26 |
| Hexagon | side 2 | 10.3923 | 12 |
Frequently asked questions
What is the difference between area and perimeter?
Area measures the surface a shape covers, in square units. Perimeter is the distance around its edge, in plain units of length.
Why is the ellipse perimeter marked approximate?
An ellipse perimeter needs an elliptic integral and has no simple exact formula, so Ramanujan’s approximation is used, which is very close.
Can I find a triangle area with only three sides?
Yes. Enter the three sides in the three-sides option and Heron’s formula gives the area, provided the sides satisfy the triangle inequality.
Which height do I use for a parallelogram?
Use the perpendicular height between the two parallel bases, not the length of the slanted side. The slanted side only affects the perimeter.
Does this calculate the volume of a cube or cylinder?
No, this page handles flat shapes only. Use the volume calculator for boxes, cylinders, cones and spheres.