Volume Calculator
Calculate the 3D volume, total surface area, and capacity of standard geometric solids with instant unit conversions.
Volume Formulas for Common Geometric Solids
Volume quantifies the 3-dimensional space enclosed within a closed boundary or occupied by a physical object. Depending on the shape, standard Euclidean geometric formulas allow precise calculation:
For deeper analysis and related planning, you can also explore our Area Calculator and Triangle Calculator.
| Shape | Volume Formula | Surface Area Formula |
|---|---|---|
| Cylinder | V = π × r² × h | A = 2πr(r + h) |
| Rectangular Box | V = l × w × h | A = 2(lw + lh + wh) |
| Sphere | V = (4/3) × π × r³ | A = 4πr² |
| Cone | V = (1/3) × π × r² × h | A = πr(r + √(r² + h²)) |
| Cube | V = s³ | A = 6s² |
| Square Pyramid | V = (1/3) × a² × h | A = a² + 2a√(a²/4 + h²) |
| Capsule | V = π × r² × (4/3 r + a) | A = 2πr(2r + a) |
Volume Unit Conversion Standards
Calculating volume often requires converting between cubic distance measurements and fluid capacity:
- 1 Cubic Meter (m³) = 1,000 Liters = 1,000,000 cm³ = 35.3147 ft³
- 1 Liter (L) = 1,000 cm³ = 0.264172 US Gallons
- 1 Cubic Foot (ft³) = 1,728 in³ = 28.3168 Liters = 7.48052 US Gallons
- 1 US Gallon = 231 cubic inches = 3.78541 Liters
Frequently Asked Questions
What is the formula for the volume of a cylinder?
The volume of a cylinder is V = π × r² × h, where r is the circular base radius and h is the cylinder height.
How do you calculate the volume of a sphere?
The volume of a sphere is V = (4/3) × π × r³, where r is the radius from the center to the outer surface.
How many liters are in one cubic meter?
There are exactly 1,000 liters in one cubic meter (1 m³ = 1,000 L).
What is the difference between volume and capacity?
Volume measures the 3D space an object occupies (often expressed in cubic meters, cubic feet, or cubic inches). Capacity measures the maximum fluid volume a hollow container can hold (expressed in liters, milliliters, or gallons).
How do I calculate volume if dimensions have different units?
Always convert all linear dimensions (length, width, height, radius) to the exact same unit (e.g., all in meters or all in centimeters) before applying the volume formula. This calculator handles unit consistency automatically.