Calculate the volume of a cylinder using its inner radius and height
Radius (R)
Height (H)
Keep decimals
Calculation result
Welcome to the Cylinder Volume Calculator! This is a free, convenient, and accurate online tool designed for students, teachers, engineers, designers, and anyone who needs to calculate the volume of a cylinder. Whether you're solving a geometry problem, calculating container capacity, or estimating materials for a project, you can get results in seconds. Simply enter the radius of the base and the height of the cylinder, and our tool will instantly calculate the volume for you, providing detailed step-by-step instructions.
The volume of a cylinder refers to the amount of three-dimensional space it occupies. Simply put, it is the total amount of liquid a cylindrical container can hold. The calculation formula is very intuitive, derived from the geometric principle of base area multiplied by height.
Core Calculation Formula:
Volume(V) = π × Radius(r)² × Height(h)
Explanation of each element in the formula:
V: Represents the volume of the cylinder. The result is usually expressed in cubic units (e.g., cubic meters m³, cubic centimeters cm³, liters L, etc.).
π: Pi, is an important mathematical constant, approximately equal to 3.14159. For convenience in calculation, 3.14 or 22/7 is sometimes used. This calculator uses a high-precision value of π to ensure maximum accuracy of the results.
r: Represents the radius of the circular base of the cylinder. This is the distance from the center of the circle to any point on its circumference. Please note: If you know the diameter (d), you must first divide it by 2 to get the radius (r = d / 2) before entering it.
h: Represents the height of the cylinder, which is the perpendicular distance between the two bases.
Important Note: When calculating, please ensure that the radius (r) and height (h) use the same unit of length (e.g., both in centimeters or both in meters). Otherwise, the calculation result will be incorrect.
Let's assume we have a cylinder with a base radius of 5 cm and a height of 10 cm. Let's calculate its volume step by step.
Calculate the Base Area:
The formula for the base area A is π × r².
A = 3.1416 × (5 cm)²
A = 3.1416 × 25 cm²
A ≈ 78.54 square centimeters (cm²)
Calculate the Volume:
Multiply the base area by the height to get the volume.
V = A × h
V = 78.54 cm² × 10 cm
V = 785.4 cubic centimeters (cm³)
Conclusion:
Therefore, the volume of this cylinder is approximately 785.4 cubic centimeters.
Using this tool requires only three simple steps:
Enter the Radius: Fill in the radius of the cylinder's base in the first input box.
Enter the Height: Fill in the height of the cylinder in the second input box.
Click Calculate: Click the "Calculate" button, and the result will be displayed below immediately. You can also choose different units (e.g., cm, m, inches), and the calculator will automatically handle unit conversions.
1. What should I do if I know the diameter, not the radius?
Answer: The radius is half the diameter. You need to divide the diameter value by 2 to get the radius before entering it into the calculator. For example, if the diameter is 10 cm, the radius is 5 cm.
2. What is the unit of volume? How is it converted to liters?
Answer: The unit of volume is cubic units. For liquid capacity, liters (L) are commonly used. The conversion relationship is: 1 cubic decimeter (dm³) = 1 liter (L). For example, a cylinder with a volume of 7854 cubic centimeters is equal to 7.854 cubic decimeters, meaning its capacity is approximately 7.854 liters. (Because 1 cm³ = 0.001 dm³)
3. Is this formula applicable to all cylinders? For example, an oblique cylinder?
Answer: The formula V = π × r² × h used by this calculator is default applicable to right circular cylinders (straight cylinders), where the bases are parallel and perpendicular to the sides. For oblique cylinders (where the two bases are parallel but not perpendicular to the sides), the formula still applies, but the height (h) here refers to the perpendicular distance (shortest distance) between the two bases, not the length of the slanted side.
4. Are there any requirements for the units during calculation?
Answer: Yes. The radius and height must use the same unit. If you use centimeters for the radius, the height must also be in centimeters. The calculation result will be the cube of that unit (e.g., cubic centimeters). Our calculator usually provides a unit selection function to ensure consistency.
5. Why is my calculation result wrong/negative?
Answer: Please check your input. The radius and height must be positive numbers. If a negative result appears, it is usually because a negative value was accidentally entered. Please ensure all input values are numbers greater than zero.
6. What are the practical uses of this calculator in daily life?
Answer: The applications are very extensive! For example:
We hope this Cylinder Volume Calculator becomes a helpful assistant in your study and work! If you have any questions, please feel free to contact us using the feedback function within the tool.
