mathematics calculator
Cylinder Volume Calculator
Calculate a right circular cylinder's volume, base area, curved lateral area, and total closed surface area.
Cylinder Volume Calculator
Cylinder volume
Enter the base radius and perpendicular height of a right circular cylinder.
This tool models an ideal closed right circular cylinder; wall thickness, open ends, and usable-capacity allowances are not included.
Formula version 1.0.0
How to use this calculator
- Enter positive base radius and perpendicular height in one unit.
- Select Calculate.
- Review circular base and curved lateral areas.
- Read volume and total closed surface area.
Symbols and units
| Symbol | Meaning | Unit or domain |
|---|---|---|
r | Base radius | length |
h | Perpendicular height | length |
V | Cylinder volume | cubic length |
S | Total closed surface area | square length |
Checked examples
Radius three, height four
Inputs: r=3, h=4
Calculation: V=π×3²×4; lateral=2π×3×4; S=lateral+2π×3²
Result: V=36π; S=42π
Total area includes both circular ends.
Check: cylinder-volume-core.test.ts
Unit cylinder
Inputs: r=1, h=1
Calculation: V=π; S=2πrh+2πr²
Result: V=π; S=4π
The base, top, and curved surface are included.
Check: cylinder-volume-core.test.ts
Assumptions, rounding, and limits
- The cylinder is right and circular.
- Radius and height are positive and consistent.
- Total surface area includes both bases.
- Wall thickness and fill allowance are excluded.
Frequently asked questions
Does total area include both ends?
Yes. Curved lateral area is reported separately.
Can I enter diameter?
Convert diameter to radius by dividing by two.
How does uniform scaling affect volume?
Scaling all lengths by k multiplies volume by k³.
Sources and review
- OpenStax: Geometric Formulas — Cylinder formulas
- OpenStax: Solve Geometry Applications: Volume and Surface Area — Cylinder volume and area
- Formula version
- cylinder.volume@1.0.0
- Formula review
- Equatara formula review
- Editorial review
- Equatara editorial review
- Last verified
- 2026-10-25
- Applicability
- Ideal closed right circular cylinder.
- Next review
- On material formula/source change, or by 2028-10-25.
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Found a problem?
Report a formula, result, example, source, or accessibility issue through the calculator correction process. Do not include sensitive input values.