Free Volume of Cylinder Calculator – Accurate, Instant & Ad-Free
Enter the radius and height to calculate volume and surface area of a cylinder
Cylinder Diagram
Cylinder Properties:
• Circular base and top
• Curved lateral surface
• Radius (r) and height (h)
• Volume = π × r² × h
• Surface Area = 2πr² + 2πrh
Cylinder Volume Formula:
Volume = π × r² × h
where π ≈ 3.14159
Surface Area Formula:
Surface Area = 2πr² + 2πrh
= 2πr(r + h)
What is a Cylinder?
A cylinder is a three-dimensional shape with two circular bases connected by a curved surface. It has a constant cross-sectional area.
Examples:
- Radius=5, Height=10 → Volume ≈ 785.40 cubic units, Surface Area ≈ 471.24 square units
- Radius=3, Height=8 → Volume ≈ 226.19 cubic units, Surface Area ≈ 207.35 square units
- Radius=4, Height=6 → Volume ≈ 301.59 cubic units, Surface Area ≈ 251.33 square units
Applications:
- Container volume calculations
- Pipe and tube measurements
- Storage tank capacity
- Engineering and construction
Calculate the volume of any cylinder instantly with our Free Volume of Cylinder Calculator. Whether you’re working on a school project, designing machinery, or estimating storage capacity, this calculator provides fast, accurate results in just seconds.
At Digital Calculator, we simplify geometry and engineering math so you can focus on what matters — understanding the concept and applying it efficiently. Our Volume of Cylinder Calculator handles both right and oblique cylinders using radius and height (or diameter), delivering precise results in cubic units like cm³, m³, or in³.
What Is the Volume of a Cylinder?
A cylinder is a three-dimensional solid with two parallel circular bases connected by a curved surface. It’s one of the most common shapes in real life — from pipes and tanks to cans and columns.
The volume of a cylinder measures how much space it occupies or how much liquid or gas it can hold. It’s measured in cubic units (cm³, m³, ft³, in³, etc.).
Mathematically, the volume depends on two key measurements:
- Radius (r): the distance from the center of the circular base to its edge.
- Height (h): the perpendicular distance between the two bases.
Formula for the Volume of a Cylinder
The basic formula is:
Volume = π × r² × h
Where:
- π (pi) = 3.1416 (approximate constant)
- r = radius of the base
- h = height of the cylinder
This formula applies to right circular cylinders — where the sides are perpendicular to the bases.
Example:
If the radius = 5 cm and height = 10 cm:
Volume = π × 5² × 10
= 3.1416 × 25 × 10
= 785.4 cm³
Answer: The cylinder’s volume is 785.4 cubic centimeters.
Our calculator performs this instantly — no need to remember π or square values.
Alternative Cylinder Volume Formulas
Depending on what measurements you have (radius, diameter, circumference, or volume itself), there are several ways to find the volume.
1. Using Radius and Height
Formula:
V = π × r² × h
This is the most direct and widely used formula.
Example:
r = 3 m, h = 4 m
V = 3.1416 × 3² × 4 = 3.1416 × 9 × 4 = 113.1 m³
Result: 113.1 cubic meters
2. Using Diameter and Height
Since diameter = 2r,
V = π × (d² / 4) × h
Example:
d = 10 cm, h = 20 cm
V = 3.1416 × (100 / 4) × 20 = 3.1416 × 25 × 20 = 1570.8 cm³
Result: 1570.8 cubic centimeters
3. Using Circumference and Height
Since circumference (C) = 2πr,
r = C / (2π)
So,
V = π × (C / 2π)² × h = (C² × h) / (4π)
Example:
C = 31.4 cm, h = 10 cm
V = (31.4² × 10) / (4 × 3.1416) = (985.96 × 10) / 12.566 = 784.9 cm³
Result: 784.9 cm³
4. For Hollow (Tubular) Cylinders
If the cylinder is hollow (like a pipe), you must subtract the volume of the inner cylinder from the outer one.
Formula:
V = π × h × (R² – r²)
Where:
- R = outer radius
- r = inner radius
Example:
R = 6 cm, r = 5 cm, h = 10 cm
V = 3.1416 × 10 × (36 – 25) = 3.1416 × 10 × 11 = 345.6 cm³
Result: 345.6 cubic centimeters
How to Use the Free Volume of Cylinder Calculator
Our Volume of Cylinder Calculator is intuitive and user-friendly. Here’s how it works:
- Select your input type: choose radius, diameter, or circumference.
- Enter the height of the cylinder.
- Click “Calculate.”
- Get the exact volume displayed instantly with unit conversion options.
You can also choose to calculate the inner and outer volume for hollow cylinders.
Try the Free Volume of Cylinder Calculator now on Digital Calculator — quick, precise, and ad-free.
Step-by-Step Examples
Let’s explore more examples using different known parameters:
Example 1: Standard Cylinder
Radius = 4 cm, Height = 9 cm
V = π × 4² × 9 = 3.1416 × 16 × 9 = 452.4 cm³
Answer: 452.4 cm³
Example 2: Using Diameter
Diameter = 12 cm, Height = 20 cm
V = π × (12² / 4) × 20 = 3.1416 × 36 × 20 = 2261.9 cm³
Answer: 2261.9 cm³
Example 3: Hollow Cylinder
Outer radius = 10 cm, Inner radius = 9 cm, Height = 15 cm
V = 3.1416 × 15 × (100 – 81) = 3.1416 × 15 × 19 = 896.6 cm³
Answer: 896.6 cm³
Example 4: Using Circumference
Circumference = 62.8 cm, Height = 10 cm
V = (62.8² × 10) / (4 × 3.1416) = (3938 × 10) / 12.566 = 3135.5 cm³
Answer: 3135.5 cm³
Volume of Cylinder Formula Table
Known Parameters | Formula | Example Input | Result |
Radius & Height | π × r² × h | r=5 cm, h=10 cm | 785.4 cm³ |
Diameter & Height | π × (d² / 4) × h | d=10 cm, h=20 cm | 1570.8 cm³ |
Circumference & Height | (C² × h) / (4π) | C=31.4 cm, h=10 cm | 784.9 cm³ |
Hollow Cylinder | π × h × (R² – r²) | R=6, r=5, h=10 | 345.6 cm³ |
Conversion | 1 m³ = 1,000,000 cm³ | 0.005 m³ | 5000 cm³ |
Understanding Cylinder Geometry
To better grasp the concept, let’s recall the key elements of a cylinder:
- Bases: Two identical, parallel circles.
- Height (h): Distance between the bases.
- Radius (r): Distance from the center to the boundary of each base.
- Lateral surface: The curved surface that wraps around the cylinder.
The formula πr²h works because it multiplies the area of the base (πr²) by the height (h), giving total enclosed volume.
Real-Life Applications of Cylinder Volume
Cylinder volume calculations are essential across various industries and everyday contexts.
1. Engineering & Manufacturing
Used to determine the capacity of tanks, pipes, and mechanical parts.
2. Construction & Architecture
Helps estimate concrete volume for columns, pillars, and storage tanks.
3. Education
Students use it to understand spatial geometry and real-world modeling.
4. Logistics
Used to calculate container storage space or volume of cylindrical packages.
5. Fluid Measurement
Essential in determining liquid capacity in cylinders, tanks, and tubes.
Our Volume of Cylinder Calculator eliminates the guesswork and simplifies all these calculations.
Common Mistakes to Avoid
Even simple geometry can go wrong without care. Avoid these common errors:
- Confusing diameter and radius — remember, radius = diameter ÷ 2.
- Mixing units — convert all measurements to the same unit (e.g., cm or m).
- Forgetting π value accuracy — always use 3.1416 for reliable precision.
- Neglecting inner radius for hollow cylinders — calculate both R and r properly.
- Rounding too soon — round only at the final step for exact results.
Our calculator takes care of all these automatically, ensuring every answer is error-free.
Benefits of Using Digital Calculator’s Volume of Cylinder Tool
Our Free Volume of Cylinder Calculator offers the perfect combination of speed, accuracy, and simplicity:
- Instant results — no waiting or manual work
- Ad-free and free forever — no pop-ups, no registration
- Multiple input types — radius, diameter, or circumference
- Unit flexibility — cm³, m³, in³, ft³
- Educational step breakdown — learn how results are calculated
- Mobile-friendly interface — calculate anywhere, anytime
Try the Free Volume of Cylinder Calculator on Digital Calculator — precision made simple!
Why Choose Digital Calculator
At Digital Calculator, our mission is to make complex math easy and error-free.
Every tool we offer is:
- Free, accurate, and ad-free
- Simple and intuitive
- Educational with step explanations
- Designed for all users — from students to engineers
Calculate now with Digital Calculator — accuracy made effortless and always free.