Cylinder Surface Area Calculator

SA = 2πr² + 2πrh. Two circular ends + lateral wrap.

Inputs

Result

Loading calculator…

How to use this calculator

  • Enter radius and height.
  • Read closed + open-top + lateral surface areas.

About this calculator

A cylinder has two circular ends (each πr², total 2πr²) and a lateral surface (rectangle when unrolled, 2πr × h = 2πrh). For an open container (top removed): lateral + 1 end. For a tube (both ends open): just 2πrh. The optimal cylinder for minimum SA at given volume has h = 2r (height = diameter) — which is why most pop cans approximate this aspect ratio.

Frequently asked

Why 2πr × h for lateral?+
Unroll the cylinder: it becomes a rectangle of width = circumference = 2πr and height = h.
Optimal ratio for minimum SA?+
h = 2r (height = diameter). For 355 mL Coke can: optimal would be r ≈ 3.84 cm, h ≈ 7.67 cm. Real cans are taller for ergonomics.
Pipe surface area?+
Pipe (open both ends) = 2πrh outer + 2πr_inner × h inner. Twice the lateral if walls are thin.
Painting a cylinder?+
Use total SA / coverage rate. For a hot-water heater (50-gal, ~0.6m × 1.5m): SA ≈ 4.7 m², 1L primer covers it.
Why did Coca-Cola pick this shape?+
Originally bottle-shaped for grip. Modern cans 6.6×12.2 cm aren't SA-optimal — taller for handheld feel + display visibility.

Related calculators

More tools you might like

Hand-picked tools that pair well with this one — same audience, same intent.