Cylinder Volume Calculator Using Radius
Cylinder volume from radius uses the formula V = pi r squared h. For a cylinder with radius 7 cm and height 15 cm, multiplying pi times 49 times 15 gives 2,309.07 cm3 or 2.309 litres. Square the radius first, then multiply by pi and the height. Calculate your own cylinder volume using radius below.
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Volume of a Right Cylinder
A right cylinder is a cylinder where the sides are perpendicular (at a 90° angle) to the circular bases. The term "right" means the axis connecting the centers of the two bases is at a right angle to the bases. Most cylinders encountered in everyday life: cans, bottles, pipes: are right cylinders.
The volume of a right cylinder uses the standard cylinder volume formula: V = π × r² × h, where r is the radius of the cylinder and h is the cylinder's height.
The difference between a right cylinder and an oblique cylinder is the orientation of the axis. A right cylinder stands straight, while an oblique cylinder tilts. Both have the same volume when the perpendicular height and radius are equal.
Worked Examples Across Unit Systems
Example 1 (Metric Centimeters): For a right circular cylinder with a radius of 7 cm and a height of 15 cm:
- Base area: π × r² = π × 7² = 49π = 153.938 cm²
- Volume in cubic centimeters: V = 153.938 × 15 = 2,309.07 cm³
- Liquid capacity: 2,309.07 ÷ 1,000 = 2.309 liters (0.610 US gallons).
Example 2 (Large Scale Metric Meters): For an architectural concrete pillar or water tank with radius 0.5 meters and height 2 meters:
- Base area: π × 0.5² = 0.25π = 0.7854 m²
- Volume in cubic meters: V = 0.7854 × 2 = 1.571 m³
- Fluid capacity: 1.571 × 1,000 = 1,570.80 liters (414.97 US gallons).
Example 3 (Imperial Inches): For a cylindrical canister with a radius of 3 inches and a height of 8 inches:
- Base area: π × 3² = 9π = 28.274 in²
- Volume in cubic inches: V = 28.274 × 8 = 226.19 cubic inches
- US Gallon conversion: 226.19 ÷ 231 = 0.979 US gallons (3.707 liters).
Example 4 (Imperial Feet): For a vertical grain silo or water tower with radius 2 feet and height 6 feet:
- Base area: π × 2² = 4π = 12.566 ft²
- Volume in cubic feet: V = 12.566 × 6 = 75.40 cubic feet
- Gallon capacity: 75.40 × 7.48052 = 563.97 US gallons (2.793 cubic yards).
Precision and Measurement Best Practices
When calculating cylinder volume from physical measurements, ensure the radius and height use identical measurement units before multiplying. Measuring internal dimensions provides true holding capacity, while measuring external dimensions determines total displaced solid volume.
Standard radius and height geometry
This tool calculates volume from the base radius and height. It uses the standard math formula. Enter your values to get instant results in metric and imperial units.
If you know the total volume and need to work backward to solve for dimensions, follow our step-by-step guides on how to find the radius of a cylinder and how to find the height of a cylinder from volume.
Base circle area multiplied by depth
The standard formula is V = pi r squared h. First square the radius. Next multiply by pi. Finally multiply by the height to get the total volume.
Frequently Asked Questions
What exactly is the radius of a cylinder?
The radius is the straight, linear distance measured from the absolute center point of the circular base outwards to the very edge of the metal or plastic wall.
How do you calculate cylinder volume using radius?
Use the standard formula: Volume = Pi (3.14159) × Radius squared × Height.
If I double the radius, how much volume do I gain?
Because the dimensional radius is mathematically squared (r²) inside the geometric formula, physically doubling the radius actually quadruples (4x) the total capacity.
How do I find the radius if I only know the diameter?
That translates to incredibly simple math. Take your exact diameter measurement and divide it cleanly by 2. The resulting quotient is your exact radius.
Which is more accurate to measure: radius or diameter?
In physical construction, measuring the total diameter across a pipe is easiest. However, in pure mathematical drafting, mapping the radius from the center point rules supreme.