Cylinder Calculator
Calculate volume, lateral surface and surface area of a cylinder. Online calculator with solution path and worked examples.
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.
Does the calculator show the working steps?
Yes. In addition to the final result the calculator displays the intermediate steps so you can follow the solution — ideal for school, university or homework.
Guide
Quick Answer
The cylinder calculator computes the volume, lateral surface and total surface area of a cylinder from radius and height.
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 · E-E-A-T
Official sources
Calculations are based on applicable German laws and official data:
Full methodology at Methodology.
Mathematics
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