Cylinder Calculator
This cylinder calculator works from any two known values: choose what you have, enter the numbers, and it finds every other quantity with the working shown.
Example: Known values: Radius and height · Radius r 5 · Height h 20 · Length unit: Centimetres (cm) → Volume V: 1,570.8 cm³. Source: Wolfram MathWorld – Cylinder: volume, lateral and surface area. Updated: .
How it is calculated
To work out a cylinder you need its radius r and height h: volume V = πr²h, lateral area = 2πrh, total surface area A = 2πr² + 2πrh. If you know other values – say volume and height – the cylinder calculator rearranges the formulas and finds r or h first.
Cylinder formulas
- Base area = πr² · Circumference C = 2πr = πd
- Volume V = base area × h = πr²h
- Lateral area = C × h = 2πrh
- Total surface area A = 2πr² + 2πrh = 2πr(r + h)
Rearranging the formulas
- Height from volume: h = V ÷ (πr²) · Radius from volume: r = √(V ÷ (πh))
- Height from lateral area: h = L ÷ (2πr) · Radius from lateral area: r = L ÷ (2πh)
- Height from surface area: h = A ÷ (2πr) − r
- Radius from surface area and height: 2πr² + 2πhr − A = 0 is a quadratic; only the positive root r = (−h + √(h² + 2A/π)) ÷ 2 makes sense.
Example: how many gallons does a drum hold?
A drum 22.5 in across and 33.5 in tall has r = 11.25 in, V = π × 11.25² × 33.5 ≈ 13,320 in³ ≈ 218 litres ≈ 57.7 US gallons – a standard 55-gallon drum with a little headroom. In metric: 60 cm across, 90 cm tall → V ≈ 254,469 cm³ ≈ 254 litres.
Other solids – boxes, spheres, cones or pipes – are covered by the volume calculator. For a single circle area use the calculator with π, and to get the weight of a solid cylinder use the density calculator.
Frequently asked questions
How do you find the volume of a cylinder?
V = πr²h. With a 5 cm radius and 20 cm height: π × 25 × 20 ≈ 1,570.8 cm³ ≈ 1.57 litres. If you have the diameter, halve it first.
What is the surface area of a cylinder?
A = 2πr² + 2πrh – two circles (top and bottom) plus the lateral surface. For r = 5 cm and h = 20 cm: 157.1 + 628.3 ≈ 785.4 cm².
How do I find the height of a cylinder from its volume?
h = V ÷ (πr²). Example: 1,570.8 cm³ ÷ (π × 25) ≈ 20 cm. From the lateral area: h = L ÷ (2πr).
How many gallons are in a cylinder?
Work out the volume in cubic inches and divide by 231 (1 US gallon = 231 in³), or in cubic feet and multiply by 7.48.
How do you calculate the lateral surface area?
Lateral area = 2πrh = circumference × height. It is the rectangle you get when you unroll the side – like the label on a can.
Sources and legal basis
- Wolfram MathWorld – Cylinder: volume, lateral and surface area
- Wolfram MathWorld – Quadratic formula (radius from surface area)
- NIST SP 811: NIST SP 811, Appendix B – Conversion factors (inch, foot, litre)
As of:
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