Math

Area Formula Calculator

Every Area Formula You Need

This calculator is a comprehensive reference for area formulas across all standard geometric shapes. Select the shape, plug in your numbers, and watch the formula come to life with step-by-step substitution.

A = l × w

Area Calculation Tips

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Try an Example

Pick a scenario to see how the calculator works, then adjust the values

Living Room Floor

Calculate the floor area of a 5m x 3m rectangular living room.

Key values: Rectangle · 5m x 3m · 15 m²

Circular Garden

Find the area of a circular garden bed with a 5-meter radius.

Key values: Circle · Radius: 5m · ≈78.54 m²

Triangular Plot (SSS)

Calculate the area of a triangular land plot with sides 3, 4, and 5 meters using Heron's formula.

Key values: Triangle (SSS) · Right triangle · 6 m²

Hexagonal Patio

Find the area of a regular hexagonal patio with 10m sides.

Key values: Regular Polygon · 6 sides · 10m per side

Documentation

This calculator is also known as Area Formula Calculator.

Read the complete guide

Why Area Formulas Matter

Area formulas are among the most fundamental tools in mathematics. They connect abstract geometry to real-world measurement problems. Every area formula can be derived from basic principles -- rectangles from counting unit squares, triangles from halving parallelograms, and circles from integral calculus or limiting polygon approximations.

Examples

Heron's Formula for a Scalene Triangle

A triangle with sides a = 7, b = 8, c = 9.

Semi-perimeter s = (7+8+9)/2 = 12. Area = sqrt(12 x 5 x 4 x 3) = sqrt(720) = 26.83 square units.

Key takeaway: Heron's formula is essential when you know all three sides but not the height.

Master Area Formulas

Build your understanding systematically:

Start with rectangles (A = l x w), then learn that triangles are half of parallelograms
Understand that all polygon areas can be decomposed into triangles
Practice with Heron's formula -- it is the most versatile triangle formula
Remember that area scales with the square of linear dimensions

Frequently Asked Questions about Area Formula Calculator

Which area formula should I use for a triangle?

Use A = 1/2 x base x height when you know both. Use Heron's formula (sqrt(s(s-a)(s-b)(s-c))) when you know all three sides. Use A = 1/2 x a x b x sin(C) when you know two sides and the included angle.

How does the regular polygon formula work?

A regular polygon with n sides of length s has area A = (1/2) x n x s^2 x cot(pi/n). This formula works by decomposing the polygon into n congruent isosceles triangles. As n increases, the polygon approaches a circle.