Geometry

Cylinder Volume Calculator

Calculate cylinder volume from radius or diameter and height. Get results in cubic units, litres, gallons, cubic feet and cubic meters.

Input Dimension Mode

Cylinder Diameter (d)

Cylinder Height (h)

Primary Output Volume Unit

Cylinder Geometry Reference

Base Area = πr² • Volume = πr²h

Cylinder Calculation Results

Decimals:

Volume in LLive Output

125.664l

Additional Computed Dimensions

Base Area

0.126 m²

Circumference

1.257 m

Total Surface Area

1.508 m²

Equivalent Standard Volume Units

Cubic Meters (m³)

0.126 m3

Cubic Centimeters (cm³)

125,663.706 cm3

Cubic Feet (ft³ / cu ft)

4.438 ft3

Cubic Inches (in³)

7,668.47 in3

Cubic Yards (yd³)

0.164 yd3

US Liquid Gallons (gal)

33.197 us_gal

Imperial Gallons (UK gal)

27.642 imp_gal

Mathematical Formula & Step-by-Step Derivation

SI Normalized Math

General Formula:

V = π × r² × h = π × (d / 2)² × h

Live Calculation With Your Input Values:

11. Calculate Radius

Formula: r = d / 2

Substituted: r = 40 / 2 = 20 cm

Step Result: Radius = 20 cm

22. Cylinder Volume Formula

Formula: V = π × r² × h

Substituted: V = π × (20 cm (Diameter / 2))² × (100 cm)

Step Result: V = 125.664 l

Normalized to SI units: V = π × (0.2 m)² × (1 m) = 0.126 m³

33. Total Surface Area

Formula: A = 2πrh + 2πr²

Substituted: A = (2 × π × 0.2 × 1) + (2 × π × 0.2²)

Step Result: A = 1.508 m²

How to Calculate the Volume of a Cylinder

A cylinder is a three-dimensional solid with two parallel, congruent circular bases. To calculate cylinder volume, multiply the circular base area by the vertical height: V = π × r² × h.

Measure Radius or Diameter: If you know the diameter (d), divide by 2 to get radius (r = d / 2).
Square the Radius: Compute r² = r × r.
Multiply by Pi (π): Compute circular base area: Area = π × r².
Multiply by Height: Multiply base area by perpendicular height (h): V = π × r² × h.
Convert to Litres or Gallons: 1 m³ = 1,000 Litres = 264.172 US Gallons.

Cylinder Volume Formula & Diameter Form

Using Radius (r):V = π × r² × hStandard Euclidean geometric form

Using Diameter (d):V = (π ÷ 4) × d² × h≈ 0.785398 × d² × h

Worked Example: Industrial Cylindrical Storage Drum

Parameters: A cylindrical steel drum with an internal diameter of 60 cm (radius r = 30 cm = 0.30 m) and a height of 90 cm (0.90 m).

1. Radius r = 60 cm ÷ 2 = 30 cm = 0.30 m

2. Circular Base Area = π × (0.30 m)² ≈ 0.2827 m²

3. Volume in Cubic Meters = 0.2827 m² × 0.90 m = 0.2545 m³

4. Volume in Litres = 0.2545 m³ × 1,000 = 254.47 Litres

5. Volume in US Gallons = 254.47 L ÷ 3.78541 = 67.22 US Gallons

Units and Measurement Conversions

Dimension Unit	Raw Volume	Litres Conversion	US Gallons
Centimeters (cm)	cm³ (mL)	Divide by 1,000	Divide by 3,785.41
Meters (m)	m³	Multiply by 1,000	Multiply by 264.172
Inches (in)	in³	Divide by 61.0237	Divide by 231
Feet (ft)	ft³	Multiply by 28.3168	Multiply by 7.48052

Practical Notes & Guidelines

Radius vs Diameter Warning: Plugging diameter directly into πr²h instead of radius overestimates cylinder volume by 400% (4×).

Related Tools: For horizontal cylinder dip and tank capacity, use our Tank Volume Calculator; for pipes and tubes, check the Pipe Volume Calculator.

Frequently Asked Questions

How do you calculate the volume of a cylinder?▼

Multiply the area of the circular base by the height: Volume = π × radius² × height (V = πr²h).

Can I calculate cylinder volume using diameter?▼

Yes. Either divide the diameter by 2 to find radius (r = d/2), or use the direct formula: V = (π / 4) × diameter² × height ≈ 0.7854 × d² × h.

How do I calculate cylinder volume in litres?▼

Calculate volume in cubic centimeters (cm³) and divide by 1,000, or calculate in cubic meters (m³) and multiply by 1,000. 1 Liter equals 1,000 cm³ or 0.001 m³.

How do I calculate cylinder volume in gallons?▼

If dimensions are in inches, calculate cubic inches (π × r² × h) and divide by 231 to obtain US liquid gallons. If in metric litres, divide litres by 3.78541.

What is the difference between radius and diameter?▼

Diameter is the full distance straight across the widest point of a circle. Radius is the distance from the center to the edge (exactly half the diameter: r = d / 2).

Can radius and height use different units?▼

Before doing manual math, radius and height must be converted into the same unit. Our calculator handles mixed units automatically.

What is the difference between cylinder volume and surface area?▼

Volume measures the internal 3D space enclosed inside the cylinder (cubic units or litres). Surface area measures the 2D exterior outer area (2πrh + 2πr² in square units).

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