# Volume Calculator

Calculate volume for cubes, spheres, cylinders, and cones. Results in cubic feet, cubic meters, cubic yards, gallons, and liters. Free volume calculator.

## What this calculates

Calculate the volume of common 3D shapes for construction projects, material estimation, and engineering. This calculator supports rectangular boxes (cubes), spheres, cylinders, and cones, with results in multiple units including cubic feet, cubic meters, cubic yards, gallons, and liters.

## Inputs

- **Shape** — options: Cube / Rectangular Box, Sphere, Cylinder, Cone
- **Length** (ft) — min 0 — Used for rectangular box
- **Width** (ft) — min 0 — Used for rectangular box
- **Height** (ft) — min 0 — Used for box, cylinder, and cone
- **Radius** (ft) — min 0 — Used for sphere, cylinder, and cone

## Outputs

- **Volume** (ft³)
- **Volume** (m³) — 1 ft³ = 0.02832 m³
- **Volume** (yd³) — 1 yd³ = 27 ft³
- **Volume** (gal) — 1 ft³ = 7.481 US gallons
- **Volume** (L) — 1 ft³ = 28.317 liters
- **Formula** — formatted as text

## Details

Volume formulas used:

  - Rectangular Box: V = length × width × height

  - Sphere: V = (4/3)πr³

  - Cylinder: V = πr²h

  - Cone: V = (1/3)πr²h

Unit conversions:

  - 1 cubic foot = 0.02832 cubic meters

  - 1 cubic yard = 27 cubic feet

  - 1 cubic foot = 7.481 US gallons

  - 1 cubic foot = 28.317 liters

Construction applications: The rectangular box formula covers room volumes (for HVAC sizing), soil fill, and material storage. Cylinder volumes are needed for tanks, pipes, and columns. Cone volumes apply to piles of gravel, sand, and similar materials.

## Frequently Asked Questions

**Q: How do I calculate the volume of a rectangular room?**

A: Measure the length, width, and height in feet. Select 'Cube / Rectangular Box' and enter the three dimensions. The result is in cubic feet, which you can convert to other units as needed.

**Q: How many cubic feet are in a cubic yard?**

A: There are 27 cubic feet in one cubic yard (3 ft × 3 ft × 3 ft = 27 ft³). This conversion is especially important when ordering concrete, soil, or gravel.

**Q: What is the volume of a sphere with a 1-foot radius?**

A: V = (4/3)π(1)³ = 4.189 cubic feet, which equals approximately 31.3 gallons.

**Q: Why is the cone volume one-third of the cylinder volume?**

A: A cone with the same base radius and height as a cylinder contains exactly one-third the volume. This can be proven with calculus or demonstrated physically by filling a cone with water three times and pouring it into the cylinder.

**Q: How do I find the volume of a half-cylinder (trough)?**

A: Calculate the full cylinder volume using this calculator, then divide by 2. A trough or half-pipe is exactly half of a full cylinder.

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Source: https://vastcalc.com/calculators/math/volume
Category: Math
Last updated: 2026-04-21