Cylinder Volume Calculator

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Volume of a cylinder = π · r² · h — base area times height. Enter radius r and height h.

Unit:

Base radius r

Height h

Volume cylinder

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What is the volume of a cylinder and how to determine it?

The Cylinder Volume Calculator is a practical online engineering and educational tool, designed for quick calculation of the volume of solids in the shape of a straight circular cylinder. A cylinder is one of the most popular solids of revolution in the world around us. All types of sewage pipes, ring wells, grain silos, beverage cans, fuel tanks and heating boilers are designed in the shape of a cylinder.

Accurately determining the volume of a cylinder is crucial in construction (e.g. estimating the amount of concrete needed to pour a round pillar), agriculture (silo capacity) and in trade. Our calculator automatically converts the entered values (radius or diameter of the base and height) into volume in liters, cubic meters or cubic centimeters.

Formula for the volume of a cylinder

The volume of a cylinder is defined as the product of the surface area of its circular base and the height of the cylinder. The mathematical formulas are as follows:

Formula for the volume of a cylinder from the base radius (r):The most basic version of the formula: V = π r² h Where V is the volume, r is the radius of the circle at the base of the cylinder, h is the height of the cylinder, and π (Pi) is a mathematical constant (≈ 3.14159).
Formula for the volume of a cylinder from the base diameter (d):Since in practice it is easier to measure the diameter of a round hole or pipe than the radius, the formula is used: V = (π d² h) / (4) Where d is the diameter of the base of the cylinder.

Application of cylinder volume calculations in practice

Application	Cylinder type	Key dimensions	Importance of volume calculations
Rainwater tanks	Round above-ground tank	Diameter bottom, wall height	Determination of the maximum water capacity in liters.
Concreting pillars	Round supporting column	Formwork diameter, column height	Accurate estimate of the required amount of ready-mix concrete from the concrete plant (in m³).
Grain silos	Vertical cylindrical silo	Silo radius, usable height	Calculation of the maximum storage capacity for grain.
Aluminum cans	Beverage can (e.g. 330 ml)	Can diameter, can height	Packaging design in the food industry.

Step by step: how to calculate the volume of a cylinder? Examples

Here are two practical examples of calculating the capacity of cylindrical objects.

Example 1: Pouring concrete into a circular pillar (diameter calculations).On a construction site, you have a cardboard formwork for a round pillar with an internal diameter of d = 40 cm (0.4 m) and a height of h = 3 m. You want to find out how many cubic meters of concrete you need to order.

We use the formula from the diameter: V = (π d² h) / (4).
We substitute the dimensions in meters: V = (π × 0.4² × 3) / (4).
We calculate the square of the diameter: V = (π × 0.16 × 3) / (4) = 0.12π.
We calculate the result: V ≈ 0.12 × 3.14159 ≈ 0.377 m³.

Example 2: Calculating the capacity of the water tank (radius calculation).You have a round rain barrel. The radius of the bottom of the barrel is r = 50 cm (5 dm) and its height is h = 100 cm (10 dm). How many liters of water will fit in this barrel?

We convert the dimensions into decimeters: r = 5 dm, h = 10 dm.
We use the radius formula: V = π r² h.
We substitute the data: V = π × 5² × 10 = 250π.
We calculate the volume: V ≈ 250 × 3.14159 ≈ 785.4 dm³.

Frequently asked questions (FAQ)

How to convert the volume of a cylinder from cubic meters (m³) to liters?

The conversion rate is simple: 1 cubic meter (m³) is exactly 1000 liters. To convert the result from m³ to liters, simply multiply it by 1000.

What is a straight circular cylinder?

It is a cylinder in which the axes of the bases are perpendicular to the planes of these bases (the side walls rise at an angle of 90° to the bottom).

How to measure the height of an inclined cylinder?

In an inclined cylinder, the height (h) is the shortest distance between the base planes measured vertically (at right angles to the ground). This is not the side length of the diagonal sidewall.

How to calculate the total surface area of a cylinder?

The total surface area of a cylinder is the sum of the areas of two circular bases and the area of the side surface. The formula is: P_c= 2π r² + 2π r h.

How to determine the height of a cylinder given its volume and radius?

You can transform the basic formula. We calculate the height (h) by dividing the volume (V) by the base area (π r²): h = (V) / (π r²).