The Shape Area Calculator calculates the area of 11 common flat shapes using each shape’s standard formula — from a simple rectangle (length × width) to an ellipse (πab), a sector (½r²θ) or a regular polygon.
Choose the shape, enter its dimensions in any unit, and read the area in the unit you prefer. For irregular shapes, see the Irregular Shape Area and Composite Shape Area calculators listed below the tool.
Shape Area Calculator
Area of 11 flat shapes: square, rectangle, triangle, circle, parallelogram, trapezoid, ellipse, sector, ring, rhombus/kite and regular polygon.
Formula
| Shape | Area formula |
|---|---|
| Square | A = a² |
| Rectangle | A = l × w |
| Triangle | A = ½ × b × h |
| Circle | A = πr² |
| Parallelogram | A = b × h |
| Trapezoid | A = ½ × (a + b) × h |
| Ellipse | A = π × a × b |
| Sector | A = ½ × r² × θ (θ in radians) |
| Ring (annulus) | A = π(R² − r²) |
| Rhombus / kite | A = ½ × d₁ × d₂ |
| Regular polygon | A = n × s² ÷ (4 × tan(π ÷ n)) |
Where: a, b = sides or bases (ellipse: semi-axes), h = perpendicular height, r = radius, R = outer radius, θ = central angle, d₁ and d₂ = diagonals, n = number of sides, s = side length.
How the Calculation Works
Step 1: Select the shape so the calculator knows which formula to use.
Step 2: Enter the dimensions. Angles can be in degrees; the calculator converts them to radians for the sector formula.
Step 3: Read the area in square units and switch the output unit if needed.
Variables Explained
| Variable | Meaning | Unit |
|---|---|---|
| h | Perpendicular height (not a slanted side) | cm, m, in, ft |
| r, R | Radius, outer radius | cm, m, in, ft |
| θ | Central angle of a sector | degrees |
| A | Area | cm², m², in², ft² |
Example Calculation
Trapezoid
Given: bases 10 cm and 6 cm, height 4 cm
Result: A = ½ × (10 + 6) × 4 = 32 cm²
Ellipse
Given: semi-axes 6 cm and 4 cm
Result: A = π × 6 × 4 ≈ 75.40 cm²
Sector
Given: radius 5 cm, angle 60° (≈ 1.0472 rad)
Result: A = ½ × 25 × 1.0472 ≈ 13.09 cm²
Regular hexagon
Given: 6 sides of 4 cm
Result: A = 6 × 16 ÷ (4 × tan 30°) ≈ 41.57 cm²
Common Area Conversion Table
| Unit | Equivalent |
|---|---|
| 1 m² | 10,000 cm² |
| 1 m² | 10.7639 ft² |
| 1 ft² | 144 in² |
| 1 acre | 43,560 ft² |
Shape Properties
Shapes that share a formula
A rectangle and a parallelogram both use base × height; a triangle is half of that. A rhombus and a kite both use half the product of their diagonals. A circle is a special ellipse where both semi-axes equal the radius.
Dimensions Explained
Height vs slanted side
For triangles, parallelograms and trapezoids, the height is measured at a right angle to the base — not along the slanted side. Using a slanted side overstates the area.
Semi-axes of an ellipse
Enter half the longest width and half the shortest width.
Frequently Asked Questions
How do you calculate the area of a shape?
Use the formula for that shape. For shapes made of several parts, add the areas of the parts.
How do you find the area of a trapezoid?
Average the two parallel sides and multiply by the height: ½(a + b)h.
How do you find the area of a sector?
A = (θ ÷ 360°) × πr², which equals ½r²θ with θ in radians.
What is the area of a ring?
The outer circle minus the inner circle: π(R² − r²).
How do you find the area of a hexagon?
For a regular hexagon, A = (3√3 ÷ 2) × s² ≈ 2.598 × s². Use the regular polygon option with 6 sides.
