Area Calculator

How to Calculate Area

Area is the space inside the boundary of a two-dimensional shape, measured in square units (sq ft, m², cm², etc.). It answers the question "how much surface does this shape cover?"

Every geometric shape has a unique area formula. Our calculator supports 12 shapes — select one from the dropdown above and enter the required dimensions to get the area instantly with a step-by-step breakdown.

Area Formulas for All Shapes

Square

A = a² — Side length squared. Example: side = 5 → A = 25.

Rectangle

A = length × width. Example: 10 × 6 = 60.

Triangle (Base × Height)

A = ½ × b × h — Half of base times perpendicular height. Example: b = 8, h = 5 → A = 20.

Triangle (Heron's Formula — SSS)

When you know all three sides (a, b, c) but not the height:

s = (a + b + c) / 2 (semi-perimeter)

A = √(s(s−a)(s−b)(s−c))

Example: sides 3, 4, 5 → s = 6, A = √(6×3×2×1) = √36 = 6.

Circle

A = πr². If you know the diameter: A = π(d/2)². Example: r = 7 → A = 153.94.

Ellipse

A = π × a × b — where a is the semi-major axis and b is the semi-minor axis. Example: a = 10, b = 6 → A = 188.50.

Trapezoid

A = ½(a + b) × h — Average of the two parallel bases times the height. Example: bases 8 and 12, height 5 → A = 50.

Parallelogram

A = b × h — Base times perpendicular height (not the slanted side). See our dedicated Parallelogram Area Calculator for the sides-and-angle method.

Rhombus

A = a × h — Edge length times perpendicular height. Alternatively: A = ½ × d₁ × d₂ (half the product of the diagonals).

Sector

A = ½r²θ — where θ is in radians. For degrees: A = (θ/360) × πr². See our Arc Length Calculator for arc length and chord.

Ring (Annulus)

A = π(R² − r²) — Outer circle area minus inner circle area. Example: R = 7, r = 3 → A = π(49−9) = 125.66.

Regular Polygon (n-gon)

A = (a² × n) / (4 × tan(π/n)) — Works for any regular polygon with n equal sides of length a. Pentagon (n=5), hexagon (n=6), octagon (n=8), etc. See our Pentagon Calculator for dedicated pentagon properties.

Area vs. Perimeter vs. Surface Area

• Area: The 2D space inside a shape (square units)
• Perimeter: The distance around the shape's boundary (linear units)
• Surface Area: The total area of all faces of a 3D solid

Frequently Asked Questions

When should I calculate area?

Whenever you need to know how much surface a space covers — flooring, painting walls, landscaping, tiling, concrete pouring, carpet installation, or any material that covers a surface.

How do I find the area of an irregular shape?

Break the irregular shape into regular shapes (rectangles, triangles, circles), calculate each area separately, then add them together. For an irregular quadrilateral: draw a diagonal, measure the perpendicular heights to the other two corners, and use A = ½ × d × (h₁ + h₂).

What's the difference between base×height and Heron's formula for triangles?

Use ½bh when you know the base and perpendicular height. Use Heron's formula when you know all three side lengths but not the height. Both give the same result — they're just different ways to reach it.

How do I convert between area units?

Common conversions: 1 m² = 10.764 ft², 1 acre = 43,560 ft², 1 hectare = 10,000 m². Multiply your area result by the appropriate conversion factor.

Does a circle count as a polygon?

No — a polygon must have straight sides. A circle has no straight sides. However, a regular polygon with a very large number of sides (n→∞) approaches a circle, and the polygon area formula approaches πr².

What is the easiest way to calculate the area of a room?

Most rooms are rectangular: just measure length × width. For L-shaped rooms, divide into two rectangles, calculate each area, and add them together.