Area and Perimeter Calculator

How are area and perimeter calculated?

Area measures the surface a shape covers and perimeter the total length of its boundary. Flooring, paint and plaster are priced by area, while skirting, fencing and framing follow the perimeter. Choose the shape from the tabs above and enter its dimensions.

Formulas

• Rectangle: area a × b, perimeter 2 × (a + b).
• Circle: area π × r², circumference 2 × π × r. With a diameter, r = D / 2.
• Triangle: area base × height / 2. If the height is unknown but all three sides are known, Heron's formula applies.
• Trapezoid: area (bottom base + top base) / 2 × height.
• Ellipse: area π × a × b, where a and b are the semi-axes.
• Sector: area r² × θ / 2 and arc length r × θ, with the angle in radians.
• Ring: area π / 4 × (D² − d²). This gives the cross section of a pipe or hollow shaft.
• Regular polygon: area n × a² / (4 × tan(180° / n)).

Example

A 4 m by 3 m room covers 12 m² and needs 14 m of skirting. A circular platform of 5 m radius covers π × 25 = 78.54 m². A triangular plot with sides of 13, 14 and 15 m comes to 84 m² by Heron's formula.

Limits

The ellipse perimeter uses an approximation whose error is negligible in practice. The trapezoid perimeter is not given because the legs are not asked for. Split irregular areas into rectangles and triangles, calculate each one and add them up.