Cylinder Volume Calculator
Calculate cylinder volume from radius or diameter and height. See liters, gallons, surface area, and step-by-step math with custom units.
The base of a right cylinder is a flat circular disk with area equal to π multiplied by the radius squared.
Multiplying the circular base area by the perpendicular height yields the 3D interior volume.
The volume of a cylinder is calculated by multiplying its circular base area by its vertical height: V = π × r² × h. For example, a cylinder with radius 3 inches and height 10 inches holds 282.74 cubic inches (1.22 US gallons). If using diameter, divide diameter by 2 first.
Cylinder Volume Calculator Formula
| Variable | Definition | Standard Units |
|---|---|---|
| V | Interior Volume of the cylinder | in³, ft³, cm³, or m³ |
| r | Radius of the circular base (distance from center to rim) | in, ft, cm, or m |
| h | Perpendicular vertical height between circular bases | in, ft, cm, or m |
| π | Mathematical constant Pi (~3.14159265) | dimensionless |
How to Calculate the Volume of a Cylinder
To understand the cylinder formula, visualize stacking thin circular coasters on top of each other. The area of one flat circular coaster is πr². Stacking them to height h multiplies that base cross-section continuously. This gives V = πr²h. If your cylinder leans sideways (an oblique cylinder), Cavalieri’s principle guarantees that as long as the vertical perpendicular height remains the same, the held volume is identical to an upright right cylinder.
Volume of a Hollow Cylinder (Pipe or Tube Wall Material)
When sizing structural metal tubing or concrete pipes, you often need the material volume of the solid wall rather than the inner air space. A hollow cylinder has an outer radius R and an inner radius r. The solid cross-sectional ring area is A = π(R² - r²). Multiplying by the pipe length L yields V = π(R² - r²)L. To calculate how much liquid flows inside the pipe, use only the inner radius r.
Radius vs. Diameter: The Most Common Mistake
Most manufactured objects (pipes, soda cans, buckets, water tanks) are measured across their full opening—their diameter (d). The single most frequent calculation error is plugging diameter directly into πr²h, which inflates the calculated volume by 400% (since (2r)² = 4r²). Always divide diameter by 2 before squaring.
Converting Cylinder Volume to Gallons and Liters
In US customary units, 1 cubic foot equals exactly 7.48052 US liquid gallons, and 1 US gallon is defined as exactly 231 cubic inches. In metric, 1,000 cubic centimeters (cm³) equals 1 liter (L). When sizing storage vessels, knowing both cubic dimensions and liquid capacity prevents ordering undersized containers.
Common Calculation Mistakes to Avoid
- Squaring diameter instead of radius (inflates volume by 4×)
- Mixing measurement units without converting (e.g. radius in inches with height in feet)
- Using the slant length of a leaning cylinder instead of the vertical perpendicular height
- Confusing internal capacity with external dimensions on thick-walled vessels
- Premature rounding of π to 3.14 on large tanks, leading to significant volume loss
Frequently Asked Questions
How do you find the volume of a cylinder if you only have diameter?▼
How many gallons are in a cylinder?▼
How do you calculate the volume of a hollow cylinder or pipe?▼
How do you find the height of a cylinder if you know the volume?▼
Does a slanted (oblique) cylinder hold the same volume as a straight one?▼
What is the surface area formula for a cylinder?▼
Authoritative Sources & Reference Standards
- Guide for the Use of the International System of Units (SI), NIST Special Publication 811 — National Institute of Standards and Technology (NIST). Verified 2026-10-01.
Official SI unit definitions, conversion factors (Appendix B), and precision standards for cubic meters, liters, and US customary units.
- Common Core State Standards for Mathematics: High School Geometry (Geometric Measurement and Dimension HSG.GMD.A.1–3) — National Governors Association Center for Best Practices & Council of Chief State School Officers. Verified 2026-10-01.
Curricular standards for volume formulas of cylinders, pyramids, cones, and spheres, including Cavalieri’s principle.