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Pick a shape, enter its measurements, and Axiom shows the formula and working.
P = 2(l + w) · A = l × w
Choose Rectangle, Triangle, or Circle and enter positive measurements using one consistent length unit. For a triangle, supply the perpendicular height for the chosen base and all three side lengths for the perimeter, then press Calculate.
Perimeter measures the boundary; area measures the space inside. A rectangle has P = 2(length + width) and A = length × width. A triangle has A = base × perpendicular height ÷ 2 and P = side a + side b + side c. A circle has circumference 2πr and area πr², where r is half the diameter.
For a rectangle 6 cm by 4 cm, enter 6 and 4. Perimeter = 2(6 + 4) = 20 cm; area = 6 × 4 = 24 cm².
For an isosceles triangle with sides 5, 5, 6 cm, use base 6 and height 4. Area = 6 × 4 ÷ 2 = 12 cm²; perimeter = 5 + 5 + 6 = 16 cm.
With radius 3 cm, circumference = 6π cm, approximately 18.84955592 cm. Area = 9π cm², approximately 28.27433388 cm².
Area counts unit squares, so multiplying centimetres by centimetres gives cm². Perimeter is a single length, so it stays in cm.
Only if that side is perpendicular to the chosen base. Otherwise you need the altitude, not a slanted edge.
It rejects three side lengths that cannot form a triangle, because the two shorter sides must add up to more than the longest. It still treats the base and perpendicular height as typed, so it cannot check that the height matches the base you chose; supply measurements that describe the same real triangle.
Halve the diameter first. For a diameter of 10, enter radius 5. Convert mixed length units before calculating; the tool does not convert them automatically.
Use the Unit Converter before combining measurements, and the Pythagorean tool when a right triangle’s height is missing. The area and perimeter lesson helps distinguish boundary length from enclosed space. Related tools: Unit Converter, Pythagorean Theorem Calculator. Read the Perimeter & Area lesson or practice perimeter & area to build confidence without relying on a calculator.