Volume Calculator
Compute Volume with exact geometric formulas. Enter the required dimensions to see area, perimeter, or volume alongside step-by-step derivations.
Formula
Box: V = L×W×H | Sphere: V = (4/3)πr³
Volume formulas vary by shape. Results given in multiple units including cubic cm, liters, and gallons.
Worked Examples
Example 1: Rectangular Tank
Problem:Calculate the volume and capacity of a tank 2m × 1.5m × 1m.
Solution:Volume = L × W × H\nV = 2 × 1.5 × 1 = 3 m³\n\nCapacity in liters:\n3 m³ × 1000 = 3000 liters\n\nIn gallons:\n3000 × 0.264 = 792 gallons
Result:3 m³ = 3000 liters
Example 2: Basketball Volume
Problem:A basketball has diameter 24 cm. Find its volume.
Solution:Radius = 24/2 = 12 cm\n\nV = (4/3)πr³\nV = (4/3) × π × 12³\nV = (4/3) × π × 1728\nV = 7238.2 cm³\nV = 7.24 liters
Result:7238 cm³ (7.24 L)
Example 3: Ice Cream Cone
Problem:Cone: radius 3cm, height 12cm. How much ice cream fits?
Solution:V = (1/3)πr²h\nV = (1/3) × π × 3² × 12\nV = (1/3) × π × 9 × 12\nV = (1/3) × 339.3\nV = 113.1 cm³ ≈ 113 mL
Result:113 cm³ (113 mL)
Frequently Asked Questions
How do I calculate volume of a box?
Volume = Length × Width × Height. For a box 10cm × 8cm × 6cm: V = 10 × 8 × 6 = 480 cm³ = 0.48 liters.
What is the formula for sphere volume?
V = (4/3)πr³. For a sphere with radius 5cm: V = (4/3) × π × 5³ = 523.6 cm³. The radius is half the diameter.
How do I find cylinder volume?
V = πr²h. For a cylinder with radius 4cm and height 10cm: V = π × 4² × 10 = 502.7 cm³. Think of it as base area × height.
What's the difference between volume and capacity?
Volume is the space an object occupies. Capacity is how much a container can hold. They're equivalent but capacity usually refers to liquids (liters, gallons).