Geometry Calculator

Calculate area, perimeter, volume, and surface area for common 2D and 3D geometric shapes. Includes geometric formulas and step-by-step calculations.

Geometry Calculator

Shape Properties

2D Shapes: Calculate area and perimeter/circumference
3D Shapes: Calculate volume and surface area
Special: Diagonals calculated for rectangles and squares
Formulas: All calculations show the mathematical formula used

How to Use the Geometry Calculator

  1. Select Shape: Choose from 2D shapes (circle, triangle, rectangle, etc.) or 3D shapes (sphere, cube, cylinder, etc.)
  2. Enter Dimensions: Input the required measurements (radius, length, width, height, sides, etc.)
  3. View Calculations: See area/volume, perimeter/surface area, and additional properties
  4. Check Formulas: Review the mathematical formulas used for each calculation
  5. Understand Results: All measurements are shown in standard units with proper labels
  6. Try Different Shapes: Switch between shapes to compare calculations and properties

Examples and Use Cases

2D Shape Calculations

Circle (r=5): Area = 78.54
A = πr² = π × 5² = 78.54
Rectangle (8×5): Area = 40
A = l × w = 8 × 5 = 40
Triangle (b=6, h=4): Area = 12
A = ½ × base × height = ½ × 6 × 4 = 12

3D Shape Calculations

Sphere (r=3): Volume = 113.10
V = ⁴⁄₃πr³ = ⁴⁄₃π × 3³ = 113.10
Cube (s=4): Volume = 64
V = s³ = 4³ = 64
Cylinder (r=3, h=8): Volume = 226.19
V = πr²h = π × 3² × 8 = 226.19

Understanding the Results

Measurement Types

Area (2D)

Space enclosed by a shape's boundaries. Measured in square units (units²).

Perimeter/Circumference (2D)

Distance around the edge of a shape. Measured in linear units.

Volume (3D)

Space enclosed by a 3D shape. Measured in cubic units (units³).

Surface Area (3D)

Total area of all surfaces of a 3D shape. Measured in square units (units²).

Common Applications

Construction & Architecture

Floor area, wall surface area, material quantities, room volumes

Engineering & Design

Component sizing, stress calculations, fluid volumes, heat transfer

Education & Homework

Geometry problems, formula verification, concept understanding

Everyday Use

Garden planning, painting projects, storage capacity, packaging

Frequently Asked Questions

What units are used for the calculations?

The calculator uses generic units. Your results will be in whatever units you input. For example, if you enter measurements in feet, results will be in square feet (area) or cubic feet (volume).

How do I calculate the area of an irregular triangle?

For triangles, enter the base and height for area calculation. If you only know the three sides, you can use the triangle option which also shows Heron's formula calculations.

Why are there two different area methods for triangles?

The calculator uses base × height ÷ 2 for area calculation, which requires the perpendicular height. The three-sided input is used for perimeter and can verify area using Heron's formula when applicable.

What is the difference between surface area and area?

Area applies to 2D shapes (like the area of a circle). Surface area applies to 3D shapes and represents the total area of all the outer surfaces combined (like the surface area of a sphere).

Can I calculate compound shapes?

This calculator works with individual basic shapes. For compound shapes, calculate each basic shape separately and then add or subtract the areas/volumes as needed.

How accurate are the calculations?

Results are calculated using standard geometric formulas and are rounded to 4 decimal places for readability. The calculations use JavaScript's built-in mathematical precision.