Math
Cylinder Calculator
The cylinder calculator handles the forward problem (radius and height → volume and surface areas) and the reverse ones students actually get stuck on: the height from a volume, the radius from a volume, or the height from a lateral area.
Round answers stay exact in terms of π (r = 3, h = 5 gives 45π) and real units convert to liters and gallons.
Radius, diameter, or height depending on the mode above.
Height, volume (cubic units), or lateral area (square units).
Pick the unit your measurements use. Area is reported in square units and volume in cubic units.
Try an example
Result
Volume
—
- Volume (exact)
- —
- Radius, diameter, height
- —
- Lateral (curved) area
- —
- Total surface area
- —
- Base area (each end)
- —
- Longest inside diagonal
- —
More details (1 more)
- Capacity
- —
Student quick launch
Grade planning, algebra checks, and formulas students reach for most.
Study path
Use this calculator with
Follow these when you want the formula behind the answer, a short lesson, or nearby tools in the same topic.
What the cylinder calculator solves
The cylinder calculator handles the forward problem (radius and height → volume and surface areas) and the reverse ones students actually get stuck on: the height from a volume, the radius from a volume, or the height from a lateral area. Round answers stay exact in terms of π (r = 3, h = 5 gives 45π) and real units convert to liters and gallons.
Formula
How to use it
- Choose the pair you know. For reverse problems, pick the mode that names the value you want to find.
- Enter the two values in one unit (volume in cubic units, lateral area in square units) and select the unit.
- Read the volume, both surface areas, the dimensions, and the capacity in liters and gallons.
How to read the answer
Volume is base area times height, so it grows with the square of the radius but only linearly with height. The lateral area is the label wrapped around a can (a rectangle 2πr by h); the total area adds the two circular ends. The diagonal is the longest straight rod that fits inside.
Common mistakes and edge cases
- Entering the diameter as the radius — choose the diameter mode or halve it first, or the volume will be 4× too big.
- Confusing lateral area (curved side only) with total surface area (side plus both ends).
- Mixing units, such as radius in cm and height in m.
- Reverse-solving with a zero or negative volume; a cylinder needs positive measurements in every mode.
Worked examples
Radius 3, height 5 (45π)
Volume
141.3717
Diameter 10, height 5 (125π)
Volume
392.6991
Radius 2, volume 100 → height
Volume
100
Height 10, volume 500 → radius
Volume
500
Radius 3, lateral area 60 → height
Volume
90
Decimal radius 2.5, height 7.5
Volume
147.2622
Zero height (impossible)
Volume
Error
Frequently asked questions
What is the formula for the volume of a cylinder?+
V = πr²h — the area of the circular base times the height. Radius 3 and height 5 give 45π ≈ 141.37 cubic units.
How do I find the height of a cylinder from its volume?+
Divide the volume by the base area: h = V / (πr²). A 100-unit³ cylinder with radius 2 is about 7.96 units tall.
How do I find the radius from the volume and height?+
r = sqrt(V / (πh)). For V = 500 and h = 10 the radius is about 3.989.
What is the surface area of a cylinder?+
Total surface area = 2πrh + 2πr² (curved side plus two circular ends). The lateral area is just 2πrh.
How many liters does a cylinder hold?+
Compute the volume in cm³ and divide by 1000. A can with r = 3 cm and h = 5 cm holds 141.37 cm³ ≈ 0.141 L.
What is the diagonal of a cylinder?+
The longest straight line inside, from a bottom edge to the opposite top edge: sqrt(d² + h²) where d is the diameter.
About this calculator
- Written by
- mathcheck editorial team
- Last reviewed
- September 4, 2026
Method
- Uses the values entered by the user and stable formulas documented on the page.
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Last updated: September 4, 2026