Area formulas let you calculate how much flat space a 2D shape covers. This cheat sheet provides every common formula with variable definitions and a worked example for quick reference.
Complete Area Formulas Table
| Shape | Formula | Variables | Example |
|---|---|---|---|
| Circle | A = πr² | r = radius | r=7 → A=153.94 |
| Rectangle | A = l × w | l = length, w = width | 8×5 → A=40 |
| Triangle | A = ½bh | b = base, h = height | 6×4 → A=12 |
| Square | A = a² | a = side length | a=9 → A=81 |
| Trapezoid | A = ½(a+b)h | a,b = parallel sides, h = height | (8+5)×4/2=26 |
| Parallelogram | A = bh | b = base, h = perpendicular height | 7×3 → A=21 |
| Ellipse | A = πab | a,b = semi-axes | 5×3 → A=47.12 |
| Rhombus | A = ½d₁d₂ | d₁,d₂ = diagonals | 6×8/2=24 |
Circle: A = πr²
The ratio of a circle's area to its squared radius is always π. If given diameter d, use r = d/2.
Quick example: r = 10 → A = 314.16 sq units
Use the Circle Area Calculator for instant results. The 3D counterpart is the Sphere Surface Area Calculator.
Rectangle: A = l × w
Multiply length by width. This is the foundation of most practical area calculations — rooms, fields, screens.
Quick example: 12 × 8 = 96 sq units
Use the Rectangle Area Calculator or the Square Footage Calculator for room measurements. See also Rectangular Prism Surface Area and Rectangular Prism Volume.
Triangle: A = ½bh
Half of the base times the perpendicular height. Any triangle — right, acute, or obtuse — uses this formula.
Quick example: b=10, h=6 → A=30 sq units
Use the Triangle Area Calculator. For 3D triangular shapes, see the Triangular Prism Calculator.
Square: A = a²
Side squared. A square is a special case of a rectangle where length equals width.
Quick example: a=15 → A=225 sq units
Use the Square Area Calculator. The 3D equivalent is the Cube Surface Area Calculator.
Trapezoid: A = ½(a + b)h
Average the two parallel sides, then multiply by the height between them.
Quick example: a=10, b=6, h=4 → A=32 sq units
Use the Trapezoid Area Calculator. For 3D trapezoidal shapes, see the Trapezoidal Prism Calculator.
Additional 2D Shapes
| Shape | Formula | Notes |
|---|---|---|
| Parallelogram | A = bh | Like a rectangle but height is perpendicular, not the slant side |
| Ellipse | A = πab | Generalizes circle; a and b are semi-major and semi-minor axes |
| Rhombus | A = ½d₁d₂ | Half the product of the two diagonals |
| Regular polygon | A = ½Pa | P = perimeter, a = apothem |
Units Quick Reference
| Unit | Equivalent |
|---|---|
| 1 m² | 10.764 ft² |
| 1 ft² | 144 in² = 0.0929 m² |
| 1 acre | 43,560 ft² = 4,047 m² |
| 1 hectare | 10,000 m² = 2.471 acres |
Related Resources
Read How to Calculate Area: Step-by-Step Guide for detailed explanations. Use the Area Calculator hub for any shape. For 3D surface coverage, explore Surface Area Formulas and Surface Area vs Volume.