Area Calculator
Area of a rectangle, square, triangle, circle, trapezoid, parallelogram or ellipse in any unit, with the formula for each shape worked out step by step.
Area Calculator: with the default inputs, area is 12 m².
Only the dimensions for the selected shape are used; the rest are ignored.
Perpendicular height to the base, not a slanted side.
Perpendicular distance between the two parallel sides.
Perpendicular height, not the slanted side.
Half the longest width.
Half the shortest width.
- Perimeter
- 14 mOnly when the dimensions determine it (rectangle, square, circle, ellipse ≈).
Assumptions
- Worked steps are shown in meters and square meters (the internal base units); results are converted to your chosen units.
- Ellipse perimeter uses Ramanujan's second approximation.
- Perimeter is left blank when the given dimensions don't determine it.
| Shape | Area |
|---|---|
| Rectangle | length × width |
| Square | side² |
| Triangle | ½ × base × height |
| Circle | π × radius² |
| Trapezoid | ½ × (base₁ + base₂) × height |
| Parallelogram | base × height |
| Ellipse | π × a × b (semi-axes) |
How this is worked out
The formula
Rectangle A = l × w Square A = s² Triangle A = ½ × b × h Circle A = π r² Trapezoid A = ½ (b₁ + b₂) h Parallelogram A = b × h Ellipse A = π a b (a, b = semi-axes)
Open How it’s calculated above to see this worked through with your own numbers.
What you enter
- Shape
- Only the dimensions for the selected shape are used; the rest are ignored.Rectangle · Square · Triangle (base and height) · Circle · Trapezoid · Parallelogram · Ellipse
- Length
- A number.in mm, cm, m, km, in, ft, yd, mi · 0 or more · defaults to 4
- Width
- A number.in mm, cm, m, km, in, ft, yd, mi · 0 or more · defaults to 3
- Side
- A number.in mm, cm, m, km, in, ft, yd, mi · 0 or more · defaults to 5
- Base
- A number.in mm, cm, m, km, in, ft, yd, mi · 0 or more · defaults to 6
- Height
- Perpendicular height to the base, not a slanted side.in mm, cm, m, km, in, ft, yd, mi · 0 or more · defaults to 4
- Radius
- A number.in mm, cm, m, km, in, ft, yd, mi · 0 or more · defaults to 3
- Base 1 (top)
- A number.in mm, cm, m, km, in, ft, yd, mi · 0 or more · defaults to 4
- Base 2 (bottom)
- A number.in mm, cm, m, km, in, ft, yd, mi · 0 or more · defaults to 8
- Height
- Perpendicular distance between the two parallel sides.in mm, cm, m, km, in, ft, yd, mi · 0 or more · defaults to 5
- Base
- A number.in mm, cm, m, km, in, ft, yd, mi · 0 or more · defaults to 7
- Height
- Perpendicular height, not the slanted side.in mm, cm, m, km, in, ft, yd, mi · 0 or more · defaults to 3
- Semi-axis a
- Half the longest width.in mm, cm, m, km, in, ft, yd, mi · 0 or more · defaults to 5
- Semi-axis b
- Half the shortest width.in mm, cm, m, km, in, ft, yd, mi · 0 or more · defaults to 3
What you get back
- Areamain answer
- Perimeter
- Only when the dimensions determine it (rectangle, square, circle, ellipse ≈).
What this assumes
- Worked steps are shown in meters and square meters (the internal base units); results are converted to your chosen units.
- Ellipse perimeter uses Ramanujan's second approximation.
- Perimeter is left blank when the given dimensions don't determine it.
About this calculator
Area is how much flat space a shape covers, measured in square units. Every area formula on this page is a rearrangement of the simplest one — rectangle = length × width — which is why they are worth understanding rather than memorising.
How to use it
Choose the shape, fill in its dimensions (the other shapes' fields are ignored), and pick the units you want in and out. You can enter a room in feet and read the area in square meters, or a garden bed in inches and get square feet.
Where the formulas come from
- Rectangle: l × w is the definition — count the unit squares in a grid.
- Square: a rectangle whose sides match, s².
- Parallelogram: slice the slanted triangle off one end and slide it to the other; you get a rectangle with the same base and the same perpendicular height, so A = b × h. The slanted side length is not what you multiply.
- Triangle: two identical triangles fit together into a parallelogram, so a triangle is half of one: ½ × b × h.
- Trapezoid: two identical trapezoids (one flipped) make a parallelogram with base b₁ + b₂, so the trapezoid is ½(b₁ + b₂) × h — the average of the two parallel sides times the height.
- Circle: cut into thin wedges and lay them alternating to form a near-rectangle of height r and width πr (half the circumference): A = πr².
- Ellipse: a circle of radius a squashed by a factor b/a in one direction, so πa² × (b/a) = πab.
Perimeter
Perimeter is shown when the dimensions fix it: rectangles, squares and circles do; triangles, trapezoids and parallelograms don't (you'd need the slanted sides). An ellipse has no simple exact formula; the calculator uses Ramanujan's approximation, which is accurate to better than 0.02%.
Units
Area units square the length unit: 1 m² = 10,000 cm², 1 ft² = 144 in², 1 yd² = 9 ft². Converting an area by the length factor is the classic mistake — 3 ft is 1 yd, but 3 ft² is 1/3 yd², not 1 yd².
Height means perpendicular height
For triangles, parallelograms and trapezoids the height is the straight-down distance between the base and the opposite side or vertex, never the length of a slanted edge. If you only know the three sides of a triangle, use the Triangle Calculator, which applies Heron's formula.
Frequently asked questions
▸How do I find the area of a trapezoid?
Average the two parallel sides and multiply by the height: A = ½(b₁ + b₂) × h. Bases 4 and 8 with height 5 give ½ × 12 × 5 = 30.
▸What's the difference between area and perimeter?
Area is the space inside a shape (square units); perimeter is the distance around it (plain length units). A 4 × 3 rectangle has area 12 and perimeter 14.
▸How do I convert square feet to square meters?
Multiply by 0.0929 (since 1 ft = 0.3048 m, 1 ft² = 0.3048² m²). Or just switch the output unit on this calculator.
▸Do I use the slanted side or the height for a parallelogram?
The perpendicular height. Base × slanted side overstates the area unless the shape is a rectangle.
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