Cylinder Calculator
Enter radius and height to get a cylinder's volume, base area, lateral surface area and total surface area, each shown with its formula.
Result
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Formulas
Volume: V = Pi * r² * h
Base area: A = Pi * r²
Lateral surface: M = 2 * Pi * r * h
Surface area: O = 2 * Pi * r * h + 2 * Pi * r²
Note: These calculations are for informational purposes only and do not replace professional tax or financial advice. All information without guarantee.
FAQ
Frequently Asked Questions
How do I calculate the volume of a cylinder?
Volume equals pi times radius squared times height. For a cylinder with a 5 cm radius and 10 cm height, the volume is approximately 785.4 cubic centimeters.
How do I calculate the surface area of a cylinder?
Total surface area equals 2 times pi times r times (r + h), which is the sum of two circular bases and the lateral surface area.
How do I convert the cylinder volume to liters?
The calculator works without a fixed unit: if you enter radius and height in centimeters, the volume comes out in cm³, and dividing by 1,000 gives liters. Example: a pot 20 cm in diameter and 15 cm high has a radius of 10 cm and holds π × 10² × 15 = 4,712.39 cm³, or about 4.7 liters. Always enter the radius, not the diameter – otherwise the volume will be four times too large.
Guide
What is the Cylinder Calculator?
The cylinder calculator computes the volume, lateral surface and total surface area of a cylinder from radius and height.
How does the Cylinder Calculator work?
Enter the radius (or diameter) and height. Volume = pi * r squared * h. Lateral surface = 2 * pi * r * h. Total surface = 2 * pi * r * (r + h). Missing values can be computed from the known ones.
Key Data and Facts
Volume = pi * r squared * h. Lateral surface = 2 * pi * r * h. Surface area = 2 * pi * r * (r + h). 1 litre = 1,000 cm cubed.
Step-by-Step Guide
How to calculate a cylinder step by step: 1. Enter the radius (or diameter) and the height. 2. Calculate the volume: V = pi x r2 x h. This equals the base area times the height. 3. Calculate the lateral surface area: M = 2 x pi x r x h. The lateral surface is the unrolled side surface (a rectangle with width = circumference and height = cylinder height). 4. Calculate the total surface area: O = 2 x pi x r x (r + h) = lateral surface area + 2 x base area. 5. Convert units: 1 litre = 1,000 cm3 = 1 dm3. 1 m3 = 1,000 litres. 6. Practical applications: pipe volume for water lines, the contents of containers and tanks, material requirements for cylindrical components. 7. Calculate the radius from a known volume: r = square root(V / (pi x h)). Calculate the height from a known volume: h = V / (pi x r2).
Calculation Example
Cylinder with r = 10 cm, h = 25 cm: volume = 3.14159 x 100 x 25 = 7,854 cm3 ≈ 7.85 liters. Lateral surface = 2 x 3.14159 x 10 x 25 = 1,571 cm2. Total surface = 2,199 cm2.
Sources
Official sources
Calculations are based on applicable German laws and official data:
Full methodology at Methodology.
Reviewed by Konstantin Iakovlev · Last updated:
Mathematics
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