WiseCalcs

Geometry calculator

This geometry calculator finds area, perimeter, circumference, and diagonal values for common shapes using the dimensions you enter. It is meant for practical school, DIY, construction, layout, and measurement checks where a quick formula-backed answer is more useful than a symbolic proof.

Area measures covered surface. Perimeter or circumference measures distance around the outside. Diagonal helps when checking fit across a rectangle or square. These are different questions, so the largest number is not necessarily the most important one.

Shape studio

Geometry that draws itself

Pick a shape and the card redraws the measurement story: area, perimeter, and diagonal where it matters.

Shape preview

Area: 60 (Perimeter: 34)

Dimensions

Measurements

Area
60
Perimeter
34
Diagonal
13

The calculator does not convert units. Keep all dimensions in the same unit before calculating. Mixing metres and centimetres will produce a mathematically valid but practically wrong result.

How does it work?

Geometry formulas

Rectangle:A=lw,P=2(l+w),d=l2+w2Square:A=s2,P=4s,d=s2Circle:A=πr2,C=2πrTriangle:A=12bh,P=a+b+c\begin{aligned} \text{Rectangle:}\quad & A=lw, & P&=2(l+w), & d&=\sqrt{l^2+w^2}\\ \text{Square:}\quad & A=s^2, & P&=4s, & d&=s\sqrt{2}\\ \text{Circle:}\quad & A=\pi r^2, & C&=2\pi r\\ \text{Triangle:}\quad & A=\tfrac{1}{2}bh, & P&=a+b+c \end{aligned}
A
Area of the selected shape.
P
Perimeter (distance around the shape).
C
Circumference (distance around a circle).
d
Diagonal of a rectangle or square.
l, w
Rectangle length and width.
s
Square side length.
r
Circle radius.
b, h
Triangle base and height.
a, b, c
Triangle's three side lengths.

A 12 by 5 rectangle has area 60, perimeter 34, and diagonal 13.

Method & sources

Each shape uses standard school geometry formulas for area, perimeter or circumference, and diagonal where applicable. All dimensions must share the same unit — you enter the measurements yourself.

Sources

Where this method comes from — use these references to understand the formula, assumptions, and limits.

  • Geometric formulas — National Institute of Standards and Technology, verified 2026-06-10

How we calculate

  • All dimensions must use the same unit.
  • Circle formulas use radius, not diameter.
  • Triangle area uses base and height; perimeter uses the three side inputs supplied.

Rounding

Results are rounded to two decimals for display. The calculation itself uses full precision.

What this calculator does

This geometry calculator finds area, perimeter, circumference, and diagonal values for common shapes using the dimensions you enter. It is meant for practical school, DIY, construction, layout, and measurement checks where a quick formula-backed answer is more useful than a symbolic proof.

The calculator uses standard Euclidean formulas and does not attach units. If you enter metres, area is square metres; if you enter centimetres, area is square centimetres. Triangle mode assumes you provide a base, a height for area, and a third side for perimeter.

How to use it

  1. Choose the shape first.
  2. Enter only the dimensions that matter for that shape.
  3. For rectangles, use length and width; for circles, use radius; for squares, use side.
  4. For triangles, use base in length, height in width, and the third side in side.
  5. Read area first, then perimeter or circumference and diagonal where available.

A worked example

A rectangle with length 12 and width 5 has area 60, perimeter 34, and diagonal 13. The area comes from 12 × 5. The perimeter is 2 × (12 + 5). The diagonal uses the Pythagorean theorem: √(12² + 5²) = 13.

What the result means

Area measures covered surface. Perimeter or circumference measures distance around the outside. Diagonal helps when checking fit across a rectangle or square. These are different questions, so the largest number is not necessarily the most important one.

Common mistakes

  • Mixing units such as metres and centimetres.
  • Using diameter instead of radius for a circle.
  • Using triangle side length as height when they are not the same measurement.
  • Forgetting that area is in square units while perimeter is in linear units.

When it is useful

Useful for homework checks, room layouts, garden beds, material estimates, cutting plans, and any quick shape calculation where the dimensions are already known.

FAQ

Can I choose units?
No unit conversion is needed. Use any unit consistently; the result follows that unit.
Why does circle ask for radius?
The standard formulas use radius. If you know diameter, divide it by 2 first.
How is rectangle diagonal calculated?
With the Pythagorean theorem: square root of length squared plus width squared.
Does triangle mode validate a real triangle?
It calculates from the supplied base, height, and third side; it does not prove the dimensions form a valid triangle.
What should I use for square?
Use the side field. Length and width are ignored for square mode.

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