About

Miscalculating cylinder volume leads to material waste in manufacturing, incorrect fluid capacity in tank design, and failed tolerances in engine piston specs. This calculator computes the volume of any cylinder in cubic inches (in³) from radius or diameter and height inputs provided in any common linear unit. It applies the standard geometric formula V = π × r² × h, converting all inputs to inches before computation. Results include automatic cross-conversions to cm³, ft³, liters, US gallons, and fluid ounces. The tool assumes a perfect right circular cylinder. Irregular cross-sections, wall thickness offsets, or thermal expansion are not modeled.

Formulas

The volume of a right circular cylinder is computed by multiplying the area of its circular base by its height.

V = π × r² × h

When diameter is provided instead of radius:

V = π × d²4 × h

Where V = volume in in³, r = radius in in, d = diameter in in, h = height in in, and π ≈ 3.14159265359.

Unit conversion to inches is applied before calculation. Conversion factors used: 1 mm = 125.4 in, 1 cm = 12.54 in, 1 ft = 12 in, 1 m = 39.3701 in.

Output conversions: 1 in³ = 16.387064 cm³. 1 ft³ = 1728 in³. 1 US gal = 231 in³. 1 L = 61.023744 in³. 1 fl oz = 1.8046875 in³.

Reference Data

Common Cylinder	Diameter	Height	Volume (in³)	Volume (L)	US Gallons
Soda Can (12 oz)	2.6 in	4.83 in	25.6	0.42	0.11
Pint Glass	3.5 in	5.8 in	55.8	0.91	0.24
1-Quart Paint Can	4.25 in	4.75 in	67.4	1.10	0.29
1-Gallon Paint Can	6.5 in	7.5 in	248.8	4.08	1.08
5-Gallon Bucket	11.91 in	14.5 in	1614.7	26.46	6.99
Standard 55-Gal Drum	22.5 in	33.5 in	13323.8	218.35	57.68
Typical Engine Piston (V8)	4.0 in	3.48 in	43.7	0.72	0.19
3-in Schedule 40 Pipe (1 ft)	3.068 in	12.0 in	88.7	1.45	0.38
Propane Tank (20 lb)	12.0 in	18.0 in	2035.8	33.36	8.81
Water Heater (40 gal)	18.0 in	46.0 in	11706.9	191.85	50.68
Coffee Mug	3.25 in	3.75 in	31.1	0.51	0.13
Scuba Tank (80 cf)	7.25 in	26.0 in	1073.1	17.58	4.65
Grain Silo (small)	144.0 in	240.0 in	3908407.4	64048.2	16919.1

Frequently Asked Questions

Radius is the distance from the center of the circular base to its edge; diameter is twice that distance. The formula using radius is V = π × r² × h. When using diameter, substitute r = d/2, giving V = π × d²/4 × h. The result is identical. The calculator handles this conversion automatically when you select the diameter input mode.

All conversion factors are exact per international standards. 1 inch equals exactly 25.4 mm (ISO 1). 1 US gallon equals exactly 231 cubic inches (US legal definition). 1 cubic inch equals 16.387064 cm³ (derived from 2.54³). These are not approximations. Rounding occurs only in the displayed output, not during computation.

No. This calculator computes the gross external volume of a solid cylinder. For hollow cylinders (pipes, tanks), you must calculate two volumes: the outer cylinder minus the inner cylinder. The inner radius equals the outer radius minus the wall thickness. For Schedule 40 pipe, consult ASME B36.10M tables for exact inner diameters.

Engine displacement uses bore (cylinder diameter) and stroke (piston travel distance) as inputs: V = π/4 × bore² × stroke × number of cylinders. Manufacturers may report nominal displacement rounded to marketing-friendly numbers. Additionally, combustion chamber volume above the piston at TDC (top dead center) is not included in displacement calculations but affects total swept volume.

Yes, but with caveats. The geometric volume represents the maximum theoretical capacity. Real containers have meniscus effects, ullage (headspace left for thermal expansion), and internal features (baffles, dip tubes) that reduce usable volume. Industry practice typically fills tanks to 80-85% of geometric capacity for safety. The converter outputs in gallons, liters, and fluid ounces for direct fluid planning.

The calculator rejects zero and negative inputs with an error notification. A cylinder requires both a positive cross-sectional dimension (radius or diameter greater than 0) and a positive height. Geometrically, a cylinder with zero radius is a line segment with no volume, and negative dimensions have no physical meaning.