Eight shapes, eight formulas, and every one of them still trips people up on which measurement goes where.
Free math tool
Geometry Calculator
Area and perimeter for eight common shapes, with a live diagram and the formula shown.
Runs entirely in your browser. Nothing you enter is sent anywhere.
Area vs perimeter, quickly
Perimeter measures the distance around the outside edge of a shape, area measures how much surface it covers. They use completely different units for the same shape (a length unit versus that unit squared), and doubling every dimension of a shape roughly quadruples its area while only doubling its perimeter, a detail that surprises people scaling up a design or a floor plan for the first time.
Geometry calculator FAQ
Why is there no exact formula for an ellipse's perimeter?
Circle circumference has a clean formula (2πr) because every point is the same distance from the center. An ellipse has two different radii, and the exact perimeter requires an elliptic integral that has no simple closed-form expression. This tool uses Ramanujan's second approximation, accurate to within a fraction of a percent for virtually any real ellipse, rather than the exact (much harder) calculation.
How is a regular polygon's area calculated?
A regular polygon (all sides and angles equal) with n sides of length s has area (n × s²) ÷ (4 × tan(π/n)). It works by splitting the polygon into n identical triangles from the center and summing them, the tan(π/n) term comes from each triangle's apex angle.
What is the difference between this and a dedicated triangle solver?
This calculator finds a triangle's area from its base and height, the version taught first in school. A dedicated triangle solver works from any three known sides or angles (not just base and height) and finds every missing side, angle, and the area, using the law of sines and cosines. Use this one for a quick base × height problem, the dedicated tool for anything more general.
Is my data private?
Yes. Every calculation and the diagram both run in your browser. Nothing you enter is sent to a server.
Free geometry calculator by ANUPRESS
Area and perimeter measure completely different things
Perimeter is a distance, the length you’d walk tracing the outside edge. Area is a surface, how much flat space sits inside that edge. They’re not just different numbers, they’re different kinds of quantity: perimeter is measured in a plain unit like meters, area in that same unit squared. Double every dimension of a shape and its perimeter simply doubles, but its area roughly quadruples, a detail that catches people off guard when scaling a floor plan, a garden bed, or a print design up or down.
Why an ellipse’s perimeter is only ever an approximation
A circle’s circumference has an exact, simple formula because every point on it sits the same distance from the center. An ellipse has two different radii, and there is no equivalent simple formula, the exact answer requires what’s called an elliptic integral, which has no closed algebraic form at all. This calculator uses Ramanujan’s second approximation, one of the most accurate simple formulas available, typically within a tiny fraction of a percent of the true value for any realistic ellipse.
The regular polygon most calculators skip
Triangle, square, and circle formulas are everywhere, but a regular pentagon, hexagon, or octagon usually isn’t. Any regular polygon (equal sides, equal angles) splits cleanly into n identical triangles meeting at its center, which is where the formula (n × s²) ÷ (4 × tan(π/n)) actually comes from, rather than being some arbitrary rule to memorize. Increase the number of sides while holding the perimeter roughly constant and you’ll notice the shape’s area creeps closer and closer to that of a circle, which is exactly what a circle is in the limit: a regular polygon with infinite sides.