Cylinder Calculator
Enter a radius and height below to instantly get the volume and surface area of a cylinder.
Cylinder Formulas
Volume = πr²h. Surface area = 2πrh + 2πr².
A common mistake is forgetting to add both circular ends when total surface area is needed — using just 2πrh leaves out the top and bottom disks entirely. Another is squaring the diameter instead of the radius; always divide the diameter by 2 first.
Worked example
A cylinder with radius 4 and height 10.
Volume = π × 4² × 10 = π × 160 ≈ 502.65
Surface area = 2π(4)(10) + 2π(4²) = 80π + 32π = 112π ≈ 351.86
A second example, with radius 2 and height 7.
Volume = π × 2² × 7 = π × 28 ≈ 87.96
Surface area = 2π(2)(7) + 2π(2²) = 28π + 8π = 36π ≈ 113.10
Keep going
- A cylinder's volume starts with a circle's area times its height; the circle calculator isolates just that circular base on its own. Circle Calculator
- A cone with the same base and height holds exactly a third of a cylinder's volume; the cone calculator shows that relationship directly. Cone Calculator
Frequently Asked Questions
What is the formula for the volume of a cylinder?
Volume = π × r² × h, where r is the radius of the circular base and h is the height.
What is the formula for the surface area of a cylinder?
Surface area = 2πrh + 2πr² — the curved (lateral) surface plus the two circular ends.
What's the difference between lateral surface area and total surface area?
Lateral surface area (2πrh) is just the curved side, without the top and bottom circles. Total surface area adds the two circular ends (2πr²) on top of that.
Where does cylinder volume show up in real life?
Anywhere something round holds material: sizing a water tank, figuring out how much concrete a cylindrical footing needs, or estimating the capacity of a pipe or silo. Because volume comes out in cubic units, keep the radius and height in the same unit — both feet or both inches — before multiplying.
Related Calculators
- Sphere Calculator — Geometry & Trigonometry
- Cone Calculator — Geometry & Trigonometry
- Triangle Area Calculator — Geometry & Trigonometry
- Trapezoid Calculator — Geometry & Trigonometry