Volume of a pyramid

How the Volume Calculator Works

Select a 3D solid, enter its dimensions, and get the volume instantly. The calculator supports six common shapes and shows the formula with each step of the computation. All results are in cubic units matching your input.

Quick start: Select "Sphere", enter radius = 5, click Calculate. Result: V = (4/3) × π × 5³ = 523.60 units³.

Volume Formulas for 3D Solids

Each shape has a specific formula. The table below shows what you need to enter and how the volume is computed.

Solid	Formula	Dimensions needed	Example
Cube	V = a³	side (a)	a=4 64
Cuboid	V = a × b × c	length, width, height	3×4×5 60
Sphere	V = (4/3)πr³	radius (r)	r=5 523.60
Cylinder	V = πr²h	radius, height	r=3, h=10 282.74
Cone	V = (1/3)πr²h	radius, height	r=4, h=9 150.80
Pyramid	V = (1/3)Bh	base side, height	a=6, h=8 96

Unit Conversions

The calculator works with any consistent unit. Here are the most common conversions between volume units.

From	To	Multiply by
cm³	liters	÷ 1000
m³	liters	× 1000
in³	cm³	× 16.387
ft³	liters	× 28.317

Practical Examples

Example 1: Water tank Cylinder r=0.5 m, h=1.2 m
V = π × 0.5² × 1.2 = 0.94 m³ = 942 liters

Example 2: Shipping box Cuboid 60 × 40 × 30 cm
V = 60 × 40 × 30 = 72 000 cm³ = 72 liters

Example 3: Basketball Sphere r=12 cm
V = (4/3)π × 12³ = 7 238.23 cm³ = 7.24 liters

Example 4: Ice cream cone Cone r=3 cm, h=12 cm
V = (1/3)π × 3² × 12 = 113.10 cm³

Example 5: Storage cube Side 2 m
V = 2³ = 8 m³ = 8 000 liters

FAQ

What units does the calculator use?

The calculator works with any consistent unit system. Enter centimeters and the result is cm³. Enter meters and the result is m³. Just keep all dimensions in the same unit.

How do I convert cubic centimeters to liters?

Divide by 1 000. 1 liter = 1 000 cm³. So 5 000 cm³ = 5 liters. For cubic meters to liters: multiply by 1 000.

Why is a cone exactly 1/3 of a cylinder?

A cone with the same radius and height as a cylinder has exactly 1/3 the volume. This can be proven with calculus (integration of circular cross-sections) or demonstrated by pouring water from a cone into a matching cylinder three times.

Does the pyramid calculator work for non-square bases?

This calculator assumes a square base (B = a²). For rectangular, triangular, or other base shapes, calculate the base area separately and use V = (1/3) × base area × height.

How do I find volume if I only know the surface area?

You need at least one dimension. For a sphere: r = √(SA / 4π), then V = (4/3)πr³. For a cube: a = √(SA / 6), then V = a³. Surface area alone is not enough for shapes with multiple independent dimensions.

What is the volume of a sphere with diameter 10?

Radius = diameter / 2 = 5. Volume = (4/3)π × 5³ = 523.60 units³. Always enter the radius, not the diameter.

Related Tools

Area Calculator

Calculate the area of 2D shapes - squares, circles, triangles - Open calculator

Perimeter Calculator

Total boundary length for squares, rectangles, circles, and more - Open calculator

Pythagorean Theorem Calculator

Find the missing side of a right triangle - Open calculator

Proportion Calculator

Solve proportions and find unknown values - Open calculator

Quadratic Equation Calculator

Solve ax² + bx + c = 0 with discriminant and vertex - Open calculator

Parameters