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VolumeCalcKit
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.

Instant results
Real-time calculation
Accurate & reliable
Standard SI formulas
Free to use
No sign up required
r (radius)h (height)
Technical Dimension Schematic100% Vector
Input Dimension Mode
Cylinder Geometry Referencer (radius)h (height)

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 Standard 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
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

Common Use Cases

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

Related Tools: For hollow conduit pipelines, use our Pipe Volume Calculator; for horizontal cylinder dip and liquid storage, use the Tank Volume Calculator; for general solids, use the Volume Calculator; and for metric volume calculations, try the Cubic Meter Calculator (m³).

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.

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

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 cubic meters (m³)?
Measure radius (or diameter) and height in meters. Volume in cubic meters (m³) = π × (radius in meters)² × (height in meters). To convert m³ to litres, multiply by 1,000.
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).
What is the difference between a cylinder and a pipe?
A solid cylinder has full internal volume. A pipe is a hollow cylinder with wall thickness, where internal capacity is calculated exclusively from the inside diameter (ID).
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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