Area Calculator
Calculate the area of a square, rectangle, triangle, parallelogram, trapezoid, rhombus, circle, sector, or ellipse — just pick a shape and the formula does the rest.
Area formulas by shape
| Shape | Formula |
|---|---|
| Square | Area = side × side |
| Rectangle | Area = width × height |
| Triangle | Area = base × height ÷ 2 |
| Parallelogram | Area = base × height |
| Trapezoid | Area = (top base + bottom base) × height ÷ 2 |
| Rhombus | Area = diagonal 1 × diagonal 2 ÷ 2 |
| Circle | Area = π × radius2 |
| Circular sector | Area = π × radius2 × (central angle ÷ 360) |
| Ellipse | Area = π × semi-major axis × semi-minor axis |
The area's unit is the square of whatever length unit you entered (e.g. enter values in cm and the result is in cm²).
What Is Area Calculation?
Every shape has its own formula, and the measurements you need change accordingly: width and height for a rectangle, radius for a circle, or the two parallel sides plus height for a trapezoid. This tool covers nine shapes — square, rectangle, triangle, parallelogram, trapezoid, rhombus, circle, sector, and ellipse — and only shows the input fields that shape actually requires.
One thing to watch is units. Since no unit is fixed, entering lengths in centimeters gives you a result in square centimeters, and so on. For shapes that need several measurements, make sure every value uses the same unit. Also remember that the height of a triangle or parallelogram must be measured perpendicular to the base, not along a slanted side.
How to Calculate Area
- Choose a shape Pick the shape you want to measure from the list. The input fields update automatically to match what that shape needs.
- Enter the measurements Fill in the lengths shown. Keep every value in the same unit, and measure height perpendicular to the base.
- Check the result and formula The area appears alongside the formula used, which is handy for checking hand calculations or understanding the method.
Tips for getting more out of it
- For a more detailed triangle calculation (e.g. finding angles from three sides), use the sister tool "Triangle Calculator". This tool is meant for the simple case where you already know the base and height.
- When a sector's central angle is 360°, its area equals the area of the full circle — you can verify this with the formula this tool uses.
- A rhombus's area can be found from its two diagonals alone — no side lengths or angles needed.
- An ellipse's area equals a circle's area (π × radius²) when its semi-major and semi-minor axes are equal.
Where Area Calculation Comes In Handy
Sizing a room or flooring materials
Figure out how much flooring or carpet you need. For irregular rooms, split the space into rectangles and triangles and add the results together.
Estimating paint or wallpaper
Divide the wall area by the coverage per can or roll listed on the product, then subtract the area of any windows.
Measuring land or garden space
Break an irregular plot into simple shapes to find the total area — useful for planning flower beds or how much sod to buy.
Checking math homework
Compare your hand-calculated answer against the tool. Since the formula is shown too, it is easy to spot exactly where a mistake happened.
Area Calculation Terms
- Base
- The reference side used in a triangle or parallelogram. Whichever side you treat as the base, using the matching height always gives the same area.
- Height
- The length measured perpendicular to the base. It is not the same as the length of a slanted side, and mixing them up throws the answer off significantly.
- Upper and lower base
- The two parallel sides of a trapezoid. Since they are added together and divided by two, it makes no difference which one you call "upper."
- Diagonal
- A line connecting two opposite vertices. A rhombus's area is found by multiplying its two diagonals and dividing by two.
- Central angle
- The angle a sector forms at the center of the circle. Its share of the full 360 degrees is exactly its share of the circle's total area.
- Pi
- The ratio of a circle's circumference to its diameter, roughly 3.14159. It appears in every area formula for circles, sectors, and ellipses.
FAQ
Side Note — Why a circle's area is "π times radius squared"
The formula for a circle's area, πr², is famously tied to Archimedes, who argued that slicing a circle into countless thin, near-triangular sectors and rearranging them produces a shape approaching a parallelogram — with a base equal to the circle's circumference (2πr) and a height equal to its radius (r). Since a parallelogram's area is base × height, that gives (2πr) × r ÷ 2 = πr², an intuitive derivation of the formula.
A sector's area formula (πr² × angle/360) simply applies the fraction of the full circle's angle (360°) that the sector covers to the full circle's area. The length of the corresponding arc follows the same logic (2πr × angle/360) — both area and arc length scale proportionally with the central angle, a core property of circles.
The formula for a trapezoid's area is recorded as far back as the Rhind Mathematical Papyrus of ancient Egypt (roughly 1650 BCE), a reminder that humans have needed to calculate the area of shapes — for land surveying and other practical purposes — since very early in recorded history.