Volume Cylinder Calculator
Fast, accurate and free online volume cylinder calculator tool running directly in your browser.
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Other tools you may find usefulCylinder volume calculator – V = πr²h with steps
A cylinder (cylinder) is a solid of revolution with a circular base. The calculator calculates the volume (V = πr²h), lateral surface area (Pb = 2πrh) and total surface area (P = 2πr² + 2πrh) for the given radius and height, with the possibility of using different units.
Cylinder formulas
Volume: V = π × r² × h. r = radius of the base, h = height. Example: r=5 cm, h=10 cm → V = π × 25 × 10 = 785.4 cm³. Lateral surface area: Pb = 2π × r × h. Base area (2 circles): Pp = 2 × π × r². Total area: P = 2π × r × (r + h). Cross-section: a circle with area π × r².
Conversion of volume units
1 m³ = 1000 L = 1,000,000 cm³. 1 L = 1000 cm³ = 1 dm³. 1 cm³ = 1 mL. Cylindrical r=5cm, h=20cm: V = π×25×20 = 1570.8 cm³ = 1.571 L. Capacity of the cylindrical tank r=50cm, h=200cm: V = π×2500×200 = 1,570,796 cm³ = 1570.8 L ≈ 1571 liters.
Applications of the roller
Containers: cans, bottles, cylindrical tanks. Pipelines: volume of water in the pipe (r=5cm, h=100m = 785 L). Engines: internal combustion engine cylinder (displacement). Shafts: moment of inertia of the cylinder. Architectural columns. Concrete mixer: calculate how much concrete it will hold.
Cylinder in practice
Coke can 330 ml: r≈3.3cm, h≈11.5cm → V=π×10.89×11.5 ≈ 393 cm³ (different from 330 ml because there is air at the top). Round pool r=3m, h=1.2m: V=π×9×1.2 ≈ 33.9 m³ = 33900 liters. Gas in the cylinder (r=15cm, h=50cm): V=π×225×50 ≈ 35343 cm³ = 35.3 L.
Frequently asked questions
How to calculate the volume of a cylinder without a calculator?
Quick approximation: π ≈ 3.14 (or 22/7). V ≈ 3.14 × r² × h. Example: r=10, h=5 → V ≈ 3.14 × 100 × 5 = 1570 (exactly 1570.8). For approximations: π ≈ 3 gives a result with an error of ~4.5%. Faster: 3 × r² × h, then add 5%.
How to calculate the capacity of a cylindrical tank?
Vertical tank: V = π × r² × h (full). Partial fill: V_partial = π × r² × h_liquid. Lying cylinder (horizontal): complicated - requires integration. For a lying person: the tool gives a formula with the arccos function. Propane tank: cylindrical cylinders - calculate by weight (LPG density 0.5 kg/L).
What is a truncated cylinder (frustum)?
Truncated cylinder (truncated cone cylinder?): otherwise known as frustum of cone. Cut cylinder: a cylinder cut at an angle. Volume of the truncated cylinder: V = π × r² × h_avg (h_avg = average height). Frustum (truncated cone): V = (π×h/3)×(r1²+r1×r2+r2²).
How is a cylinder used in car engines?
Displacement: cylinder volume = key engine parameter. V_stroke = π × (bore/2)² × stroke × number_of_cylinders. 2.0 L engine = 2000 cm³ total capacity. Bore = cylinder diameter, Stroke = piston stroke. Compression ratio: V_max/V_min. Larger capacity: usually more power (but not always).
How to calculate the amount of paint to paint a cylinder?
Calculate the lateral surface area: Pb = 2π × r × h. If you are painting from the outside: only Pb (without covers). If painting the tank: Pb + 1 or 2 × π × r². Example tank r=1m, h=2m: Pb = 2π×1×2 = 12.57 m². 1 L of paint = 10-12 m² → you need ~1.2 L (one layer).
Related tools: volume calculator, cone calculator and sphere calculator.