cylinder calculator
Compute cylinder volume, lateral area, total surface, base area, circumference, and optional mass by entering radius or diameter and height. Built for engineers, technicians, and students who need fast, accurate, unit-aware results.
Input
All dimensions are interpreted in this unit.
Choose whether you will enter radius or diameter.
Number of decimal places in results (0–10).
Enter a non-negative value in the selected unit.
Vertical height of the cylinder.
Provide material density to compute mass.
Results
Volume
—
m³
Lateral Surface Area
—
m²
Total Surface Area
—
m²
Base Area
—
m²
Circumference
—
m
Mass (optional)
—
kg
Authoritative data source & methodology
Primary reference: Wolfram MathWorld — Cylinder (accessed 2025), and ISO 80000-1:2022 (Quantities and units) for symbols and unit usage.
- MathWorld entry: Cylinder — MathWorld
- ISO 80000-1:2022: Quantities and units — Part 1
All calculations strictly follow the formulas and conventions provided by these sources.
The formula, explained
Volume: \[ V=\pi r^2 h \]
Lateral surface: \[ A_L = 2\pi r h \]
Total surface: \[ A_T = 2\pi r (r+h) = A_L + 2\pi r^2 \]
Base area: \[ A_B = \pi r^2 \] Circumference: \[ C = 2\pi r \] If density \( \rho \) is given, mass: \[ m = \rho \, V \]
Glossary of variables
- r — radius of base circle
- d — diameter, \( d = 2r \)
- h — height of the cylinder
- V — volume
- AL — lateral surface area (side only)
- AT — total surface area (side + two bases)
- AB — base area
- C — circumference of the base
- \(\rho\) — density; mass \( m=\rho V \)
How it works: a step-by-step example
Inputs: unit = m, mode = radius, \( r = 0.25\,\text{m} \), \( h = 1\,\text{m} \), density omitted.
- Compute base area: \( A_B = \pi r^2 = \pi \times 0.25^2 \approx 0.19635\,\text{m}^2 \).
- Volume: \( V = A_B \times h \approx 0.19635 \times 1 = 0.19635\,\text{m}^3 \).
- Lateral area: \( A_L = 2\pi r h \approx 2\pi \times 0.25 \times 1 \approx 1.57080\,\text{m}^2 \).
- Total surface: \( A_T = A_L + 2A_B \approx 1.57080 + 0.39270 = 1.96350\,\text{m}^2 \).
- Circumference: \( C = 2\pi r \approx 1.57080\,\text{m} \).
Frequently asked questions
Should I enter radius or diameter?
Choose either. If you enter diameter, the tool converts internally using \( r=d/2 \).
Which unit should I pick?
Pick the unit of your dimensions (mm, cm, m, in, ft). The calculator converts to SI internally and reports results with the appropriate squared or cubed unit.
What is lateral surface area?
The side surface only, excluding the two bases. Use total surface if you need the full exterior area.
How is mass computed?
Mass equals density times volume: \( m=\rho V \). Provide density in common units (kg/m³, g/cm³, lb/ft³).
Does this support oblique cylinders?
No. This calculator is for right circular cylinders. For oblique shapes, lateral area differs.
Can I copy or print results?
Yes. Use the “Copy results” or “Print” buttons under the input section.
Tool developed by Ugo Candido. Content verified by CalcDomain Editorial Board.
Last accuracy review: