# Cylinder Surface Area Calculator

> Find a cylinder’s curved (lateral) area, end area, total closed surface and open-top surface from its radius or diameter and height.

Category: Algebra, geometry & advanced math · Applies to: Worldwide · Last updated: 2026-10-29
Interactive calculator: https://calculators.geekmidst.com/calculators/cylinder-surface-area-calculator

A cylinder’s surface is a rolled-up rectangle (2πr × h) plus two circular ends. Pick the version you need: curved side only, open-topped or closed.

Also called: Curved surface area of cylinder calculator.

## Inputs
- I know the (options: Radius, Diameter; default radius)
- Radius or diameter (default 3)
- Height (default 10)
- Length unit (options: Millimetres (mm), Centimetres (cm), Metres (m), Kilometres (km), Inches (in), Feet (ft), Yards (yd), No unit (plain numbers); default cm)

## Results
- Total surface area (closed)
- Lateral (curved) area 2πrh
- Each circular end πr²
- Open-top surface (side + one end)
- Volume πr²h

## Formula

```
Lateral = 2πrh;  End = πr²;  Total = 2πrh + 2πr² = 2πr(r + h);  Open top = 2πrh + πr²
```

Where:
- r: radius (half the diameter)
- h: height

## Worked example
1. Lateral = 2π × 3 × 10 = 60π ≈ 188.495559 cm².
2. Each end = π × 3² = 9π ≈ 28.274334 cm².
3. Total = 60π + 18π = 78π ≈ 245.044227 cm².

**Result:** A closed cylinder 3 cm in radius and 10 cm tall has a surface area of about 245.04 cm².

## What the result means

Use the lateral area for a label or pipe insulation, the open-top figure for a cup or tank without a lid, and the total for a sealed can.

## Assumptions and limits
- A right circular cylinder: the sides are perpendicular to circular ends.
- Sheet thickness, seams and overlaps are ignored.
- For material orders, add an allowance for seams and waste.

## Questions

### Why is the curved area 2πrh?

Unroll the side and it is a rectangle whose width is the circumference 2πr and whose height is h.

### How does a pipe with no ends work?

Use the lateral area only; for the inside and outside of a thick pipe, use each radius separately.

## Related calculators
- [Surface Area Calculator](https://calculators.geekmidst.com/calculators/surface-area-calculator)
- [Volume Calculator](https://calculators.geekmidst.com/calculators/volume-calculator)
- [Cone Surface Area Calculator](https://calculators.geekmidst.com/calculators/cone-surface-area-calculator)

Source: GM¹X CalcVerse — https://calculators.geekmidst.com/calculators/cylinder-surface-area-calculator