Cylinder Volume Formula: Calculate with Ease

This calculator works out the volume of a cylinder when you enter its radius (or diameter) and height. You get the volume in cubic units, which you can then convert to liters or gallons if needed. The formula is V = πr²h, where r is the radius and h is the height.

Formula

The volume of a cylinder is the amount of space inside it. The standard formula is:

V = π × r² × h

• V = volume (cubic units, e.g., cm³, m³, in³)
• π (pi) ≈ 3.14159
• r = radius of the circular base (same unit as height)
• h = height of the cylinder (same unit as radius)

If you only know the diameter (d), use r = d/2. The formula becomes V = π × (d/2)² × h = (π/4) × d² × h.

Worked Example

Using the default values from the calculator above: radius = 5 cm, height = 10 cm.

1. Square the radius: 5² = 25 cm²
2. Multiply by π: 25 × 3.14159 ≈ 78.53975 cm² (this is the base area)
3. Multiply by the height: 78.53975 × 10 = 785.3975 cm³

Rounded to two decimals, the volume is 785.40 cm³. The calculator shows the same result. To get liters, divide by 1000 (since 1 L = 1000 cm³): 785.40 / 1000 = 0.785 L (rounded to three decimals).

Why the Formula Works

A cylinder is essentially a stack of identical circular disks. The area of one disk is πr². If you stack h of these disks (where h is the height), you get the total volume. This is why the formula multiplies the base area by the height. The same logic applies to any prism, but for a cylinder the base is a circle. This relationship is fundamental in geometry and is used in many real-world volume calculations, from water tanks to soda cans.

When to Use This Calculation

You need the cylinder volume formula whenever you want to know the capacity of a cylindrical object. Common examples include:

• Water tanks, fuel tanks, and propane cylinders
• Pipes and tubes (to find internal volume)
• Cans, bottles, and jars (to check capacity)
• Concrete columns or pillars (to estimate material)
• Hydraulic cylinders and pneumatic systems

For a pipe, use the inner radius (not the outer) if you want the volume of fluid it can hold. For a tank with curved ends (like a horizontal tank with elliptical heads), the formula is more complex—this calculator only works for a perfect right circular cylinder.

Common Mistakes and How to Avoid Them

One frequent error is mixing units. If the radius is in inches and the height is in feet, you must convert one to the other before using the formula. For example, convert feet to inches (1 ft = 12 in) or inches to feet (1 in = 1/12 ft). The volume will then be in cubic inches or cubic feet respectively.

Another mistake is using the diameter instead of the radius. If you have the diameter, divide it by 2 first. A related error is forgetting to square the radius—multiplying by r instead of r² will give a result that is too small by a factor of r.

Rounding too early can also cause errors. Keep at least 3-4 significant figures during intermediate steps, then round at the end. For example, using π ≈ 3.14 instead of 3.14159 changes the result by about 0.05%.

Units and Conversions

The volume you get is in cubic units of whatever you used for radius and height. Common conversions:

• 1 cm³ = 1 milliliter (mL)
• 1,000 cm³ = 1 liter (L)
• 1 m³ = 1,000 liters
• 1 in³ = 16.387 cm³
• 1 ft³ = 28.317 liters
• 1 US gallon = 3.785 liters
• 1 US gallon = 231 in³

For example, a cylinder with radius 10 cm and height 20 cm has volume π × 100 × 20 = 6,283.19 cm³, which is 6.283 liters (about 1.66 US gallons).

Limitations of the Formula

The formula V = πr²h applies only to a right circular cylinder—one where the sides are perpendicular to the base and the base is a perfect circle. If the cylinder is tilted (oblique), the volume is still the same if the height is measured perpendicular to the base, but the formula uses the vertical height, not the slant length. For a cylinder with a non-circular base (e.g., elliptical), you need a different formula. Also, if the cylinder has walls (like a pipe), you must decide whether you want the total volume (outer dimensions) or the internal volume (inner dimensions).

Practical Tips for Measuring

When measuring a real cylinder, accuracy matters. Use a caliper for small diameters; for large tanks, measure the circumference and divide by 2π to get the radius. Measure the height at several points and average them if the cylinder is not perfectly uniform. Always measure in the same unit system to avoid conversion errors. If you’re measuring a partially filled horizontal cylinder, the volume calculation is more complex—this calculator assumes the cylinder is full and upright.

Frequently Asked Questions

How do I find the volume if I only know the diameter and height? Divide the diameter by 2 to get the radius, then use V = πr²h. For example, diameter 12 cm, height 8 cm: r = 6 cm, V = π × 36 × 8 ≈ 904.78 cm³.

Can I use this formula for a pipe? Yes, but use the inner radius (or inner diameter) to get the fluid capacity. For the volume of the pipe material itself, subtract the inner volume from the outer volume.

What is the volume of a cylinder in liters? First compute the volume in cubic centimeters (cm³), then divide by 1000 to get liters. For example, 2,500 cm³ = 2.5 liters. If you have cubic meters, multiply by 1000 to get liters.

Why is pi used in the formula? Pi (π) is the ratio of a circle’s circumference to its diameter, approximately 3.14159. It appears because the base of a cylinder is a circle, and the area of a circle is πr². The formula multiplies that area by the height.

Does the formula work for any cylinder shape? It works for right circular cylinders (the usual kind). For oblique cylinders (leaning), the volume is the same if you use the perpendicular height. For elliptical or other bases, the formula changes.

How do I convert cubic inches to gallons? One US gallon equals 231 cubic inches. So divide the volume in cubic inches by 231 to get gallons. For liters, 1 gallon ≈ 3.785 liters.

Related

• How to Multiply Fractions: Step-by-Step Guide
• Hectares to Acres Australia: Convert ha to ac
• H-Index for Companies: Meaning, Calculation & Limits

in r | Radius | cm | 5 | 0
in h | Height | cm | 10 | 0
out vol | Volume | cm³ | pi * r^2 * h | 2
out liters | Volume | L | (pi * r^2 * h) / 1000 | 3