The right circular cylinder is the workhorse shape of everyday objects: cans, pipes, tanks, columns, straws, rollers, drums, batteries, silos, drinking glasses, and the piston chambers in car engines. Whether you are a student checking geometry homework, a engineer sizing a storage tank, a cook scaling a recipe for a cylindrical mold, or a builder ordering concrete for a column form, knowing the exact volume saves guesswork and wasted material.
This cylinder volume calculator takes the two measurements that fully define a right circular cylinder — the radius of its circular base and its perpendicular height — plus a Length Unit dropdown, and instantly returns the volume together with the base area, the lateral (curved) surface area, and the total surface area. The engine converts both radius and height to centimeters before applying the formulas, so all outputs come back in cm (cm² for areas, cm³ for volume). Adjust either number or switch the unit dropdown and every result updates, so you can feel how strongly the volume depends on the radius (it grows with the square of the radius) rather than the height (which is linear).
How to Use
- Measure or enter the Base Radius. The radius is half the diameter of the circular base. If you only have the diameter, divide it by two first.
- Measure or enter the Height. This is the straight perpendicular distance between the two circular ends, measured parallel to the central axis. It is not a diagonal across the side.
- Pick the Length Unit from the dropdown — Centimeters (cm), Meters (m), Inches (in), or Feet (ft). Both the radius and the height are assumed to be in this unit. The engine converts them to centimeters (1 m = 100 cm, 1 in = 2.54 cm, 1 ft = 30.48 cm) before calculating.
- Read the Volume on the highlighted result card, in cubic centimeters (cm³).
- Use the supporting readouts as needed: the Base Area (cm²) is the area of one circular disk, the Lateral Surface Area (cm²) is the area of the curved side only (unrolled, it is a rectangle of width 2πr and height h), and the Total Surface Area (cm²) adds the two circular end caps to that.
- If your project needs a capacity in gallons or liters, the engine already gives you cm³: divide by 1,000 to get liters, or divide by 3,785 to get US gallons.
A quick sanity check: a right circular cone with the same base radius and height holds exactly one-third of this cylinder's volume. If your cone result equals the cylinder result, you have forgotten the one-third factor.
The Cylinder Volume Formula
The volume of a right circular cylinder is the area of its circular base multiplied by its height:
V = π × r² × h
Where:
- V is the volume.
- r is the radius of the circular base.
- h is the perpendicular height.
- π is the constant pi, approximately 3.14159.
Because the radius is squared, doubling the radius quadruples the volume, while doubling the height only doubles it. That is why a short, wide bucket holds far more than a tall, narrow one, even when both look tall.
The surface areas follow directly:
- Base area (one end) = π × r²
- Lateral (curved) surface area = 2 × π × r × h
- Total surface area = 2 × π × r² + 2 × π × r × h = 2 × π × r × (r + h)
Worked example with r = 5 and h = 10: r² = 25, so V = π × 25 × 10 = 785.40 cubic units. The base area is π × 25 = 78.54 square units, the lateral area is 2 × π × 5 × 10 = 314.16 square units, and the total surface area is 2 × π × 5 × 15 = 471.24 square units.
Why the Squared Radius Matters
It is tempting to think of a cylinder as "a circle stretched upward," and the formula does exactly that — but the stretch only multiplies once, while the circle's own area already grows with the square of the radius. In practice, this means upgrading a pipe from radius 5 cm to radius 10 cm (the same wall thickness, the same length) quadruples the flow capacity, not doubles it. Engineers sizing pumps, storage tanks, and gutters learn early that the radius term dominates every other decision.
For an open-ended cylinder such as a pipe or a straw, you only care about the lateral surface area (the material of the wall), not the end caps. For a closed drum, you need the total surface area to know how much paint or sheet metal to buy. This calculator returns both numbers so you can pick the right one for your problem.
Examples
Example 1 — A standard cylinder. With radius 5 cm and height 10 cm, the volume is 785.40 cm³, the base area is 78.54 cm², the lateral surface area is 314.16 cm², and the total surface area is 471.24 cm². This is the built-in example and matches the classic textbook answer of about 250π cubic units.
Example 2 — A cylindrical water tank. A vertical steel tank has a base radius of 3 meters and a height of 7 meters. Pick Meters (m) from the unit dropdown, type 3 and 7. The engine converts to 300 cm and 700 cm and returns a volume of about 197,920,337 cm³ (≈ 197.92 m³). Since 1 cubic meter holds 1,000 liters, the tank carries about 197,920 liters of water. At a typical water-and-wastewater rate of roughly $0.003 per liter to fill from empty, filling the tank once costs about $594 — a useful figure before you size a pump or a delivery.
Example 3 — A large industrial silo. A silo has radius 1,000,000 units and height 2,000 units. The engine scales with no overflow and reports a volume on the order of 6.28 × 10¹⁵ cubic units, confirming the formula handles very large magnitudes without rounding errors.
Example 4 — Scaling up. Going from radius 2, height 4 (volume 50.27) to radius 4, height 4 quadruples the radius effect: the volume jumps to 201.06, four times larger — exactly as the squared-radius term predicts.
FAQ
What is the formula for the volume of a cylinder?
The volume is V = π × r² × h, where r is the radius of the circular base and h is the perpendicular height. It is the area of the circular base multiplied by the height, and it applies to any right circular cylinder.
How do I find the volume if I only know the diameter?
Divide the diameter by 2 to get the radius, then plug that radius into V = π × r² × h. For example, a diameter of 10 means a radius of 5, giving the same 785.40 cubic-centimeter result as the worked example.
What is the surface area of a cylinder?
The curved (lateral) surface area is 2 × π × r × h. The total surface area adds the two circular end caps: 2 × π × r × (r + h). This calculator returns both the lateral and the total automatically.
How do I convert cubic centimeters to gallons or liters?
One liter equals 1,000 cm³, so divide a cm³ volume by 1,000 to get liters. One US gallon equals about 3,785 cm³ (or 231 cubic inches), so divide a cubic-inch volume by 231 to get US gallons.
Why does doubling the radius quadruple the volume?
The radius appears squared in the formula, while the height appears only to the first power. If you double r, r² becomes four times larger, so the volume quadruples even with the same height. Doubling the height alone only doubles the volume.
Is this calculator for right circular cylinders only?
Yes, it assumes a right circular cylinder — the central axis is perpendicular to the circular ends. The volume formula also works for an oblique (tilted) cylinder by Cavalieri's principle, but the lateral and total surface-area readouts assume a right cylinder.
Disclaimer
This cylinder volume calculator is provided for informational purposes only and does not constitute engineering, construction, or design advice. Results are based on the standard right-circular-cylinder formulas and the exact inputs you enter; real objects such as tanks, pipes, and drums may be imperfect cylinders or may have rounded ends. Always verify critical measurements with appropriate professionals and surveying equipment before making purchasing or structural decisions.