Quick answer
Choose a shape, enter its dimensions in one unit and the calculator returns the area in that unit squared: a 5 by 3 rectangle is 15, a triangle uses half the base times the height, and a circle uses π times the radius squared.
The shapes covered are the rectangle, triangle, circle, trapezoid, ellipse, parallelogram, rhombus and regular polygon. Use one length unit for every dimension.
Related tools: Area of a Circle Calculator: Area of a circle from its radius, diameter or circumference. Area of a Trapezoid Calculator: Area of a trapezoid from its parallel sides and height. Surface Area Calculator: Surface area of a sphere, cube, cylinder, cone or box.
How to use the Area Calculator
- Choose shape: Rectangle (a × b), Triangle (base a, height b), Circle (radius a), Trapezoid (parallel sides a, b; height c), Ellipse (semi-axes a, b) and Parallelogram (base a, height b) and 2 more.
- Enter a (above 0).
- Optionally, enter b (above 0).
- Optionally, enter c (above 0).
- Optionally, enter n (sides) (a whole number, 3 or more).
- Press Calculate to see the result, and use Reset to start again.
| Input | What to enter | Allowed values |
|---|---|---|
| Shape | Choose one: Rectangle (a × b); Triangle (base a, height b); Circle (radius a); Trapezoid (parallel sides a, b; height c); Ellipse (semi-axes a, b); Parallelogram (base a, height b); Rhombus (diagonals a, b); Regular polygon (side a, n sides) | Starts at Rectangle (a × b) |
| a | A number | > 0 |
| b (optional) | A number | > 0 |
| c (optional) | A number | > 0 |
| n (sides) (optional) | A whole number | ≥ 3 |
Formula and method
Formula
rectangle ab; triangle ½ab; circle πr²; trapezoid ½(a+b)c; ellipse πab; rhombus ½ab; regular polygon n·a² ÷ (4 tan(π/n))
IEEE-754 double precision; shown to at most 6 decimal places.
Use one length unit; the area is in that unit squared.
Worked examples
These examples are verified: each one is an automated test case that the live calculator must reproduce exactly.
Example 1
Inputs: Shape = Rectangle (a × b); a = 5; b = 3.
| Result | Value |
|---|---|
| Area | 15 |
Example 2
Inputs: Shape = Triangle (base a, height b); a = 6; b = 4.
| Result | Value |
|---|---|
| Area | 12 |
Example 3
Inputs: Shape = Circle (radius a); a = 2.
| Result | Value |
|---|---|
| Area | 12.566371 |
The first line is the headline result (area). IEEE-754 double precision; shown to at most 6 decimal places.
Formulas and a quick check
A triangle is half of a parallelogram with the same base and height, which is why it has the factor ½. A trapezoid with parallel sides 8 and 12 and height 5 has area ½ × (8 + 12) × 5 = 50; a circle of radius 6 has area π × 36 = 113.10.
| Shape | Area |
|---|---|
| Rectangle | a × b |
| Triangle | ½ × base × height |
| Circle | π × r² |
| Trapezoid | ½ × (a + b) × height |
| Ellipse | π × a × b (semi-axes) |
| Rhombus | ½ × d₁ × d₂ (diagonals) |
| Regular polygon | n × s² ÷ (4 × tan(π/n)) |
Common mistakes
- Using the diameter where the formula needs the radius.
- Using a slanted side instead of the perpendicular height of a triangle or trapezoid.
- Mixing units, for example feet and inches.
Three shapes with sides a = 8, b = 12 and height c = 5
Every figure in this table comes from running this calculator, so it matches what the form returns.
| Shape | Area |
|---|---|
| Rectangle (a × b) | 96 |
| Triangle (base a, height b) | 48 |
| Trapezoid (parallel sides a, b; height c) | 50 |
What happens with invalid input
These messages are produced by the calculator itself, so you know what to fix.
- b: left empty shows "Enter this value." beside that field and no result.
- n (sides): entering "2" shows "n (sides) must be at least 3." beside that field and no result.
Choosing between the Area Calculator and similar calculators
Each row shows what a related calculator on this site asks for and what it returns, so you can pick the one that matches your question.
| Calculator | You enter | It returns |
|---|---|---|
| [Area of a Circle Calculator](/math/area-of-a-circle/) | i know the and value | Area |
| [Area of a Trapezoid Calculator](/math/area-of-a-trapezoid/) | base a, base b and height | Area |
| [Surface Area Calculator](/math/surface-area-calculator/) | shape and a | Surface area |
| [Triangle Area Calculator](/math/triangle-area-calculator/) | base and height | Area |
| [Sector Area Calculator](/math/sector-area/) | radius and central angle | Sector area |
Background: geometry measurements
Geometry results carry units that depend on the quantity: a perimeter or length is in linear units such as cm, an area or surface area is in square units (cm²) and a volume is in cubic units (cm³). Use one length unit for every input, because the calculator multiplies the numbers as given.
Flat (2D) shapes have an area and a perimeter; solids (3D) have a surface area and a volume. Two familiar checks: a circle of radius r has area πr² and circumference 2πr, and a sphere has volume (4/3)πr³ and surface area 4πr².
Assumptions and limitations
- Dimensions must be positive
If a required value is empty, not a number, or outside its allowed range, the form marks that field with a message and shows no result instead of a misleading number. The automated checks deliberately try invalid entries for b and n (sides) to confirm this.
Frequently asked questions
Why is the area of a triangle half the base times the height?
Two identical triangles fit together to make a parallelogram whose area is base times height, so one triangle is half of it.
What does the Area Calculator calculate?
Area of common two-dimensional shapes. It returns Area.
What formula does the Area Calculator use?
rectangle ab; triangle ½ab; circle πr²; trapezoid ½(a+b)c; ellipse πab; rhombus ½ab; regular polygon n·a² ÷ (4 tan(π/n)). Use one length unit; the area is in that unit squared.
What do I need to enter in the area Calculator?
You enter Shape and a. Optional: b, c and n (sides).
How is the result rounded or limited?
IEEE-754 double precision; shown to at most 6 decimal places. Dimensions must be positive.
What does the “Shape” option change?
It sets how the area is worked out. The choices are Rectangle (a × b), Triangle (base a, height b), Circle (radius a), Trapezoid (parallel sides a, b; height c), Ellipse (semi-axes a, b), Parallelogram (base a, height b), Rhombus (diagonals a, b) and Regular polygon (side a, n sides).
What is an example of a area result?
With shape Rectangle (a × b), a 5 and b 3, the area is 15.
Related calculators
- Area of a Circle Calculator — Area of a circle from its radius, diameter or circumference.
- Area of a Trapezoid Calculator — Area of a trapezoid from its parallel sides and height.
- Surface Area Calculator — Surface area of a sphere, cube, cylinder, cone or box.
- Triangle Area Calculator — Area of a triangle from base and height.
- Sector Area Calculator — Area and arc length of a circular sector.
- Parallelogram Area Calculator — Area of a parallelogram.
- Rhombus Calculator — Area, side and perimeter of a rhombus from its diagonals.
- Ellipse Calculator — Area and approximate perimeter of an ellipse.
- Orthocenter Calculator — Orthocenter of a triangle from its vertices.
Sources
- OpenStax, Prealgebra 2e (Rice University): perimeter, area, volume, circumference and the Pythagorean theorem
Content last reviewed 2026-11-04. Formulas and worked examples are checked by automated tests against independently computed values.