Cylinder calculation inputs
Select a mode, enter measurements, and choose output preferences.
Calculator guide
Interactive cylinder diagram
What each measurement represents
The radius runs from the center of a circular base to its edge. The diameter spans the full circle and equals twice the radius. Height is the perpendicular distance between the two parallel circular bases. For a horizontal tank, the same dimension is often called cylinder length.
The calculator can accept radius, diameter, circumference, or base area. It converts every input into meters internally. This avoids mixed-unit errors. The final answer is then converted to your selected output unit.
diameter = 2 × radius
circumference = 2πr
base area = πr²
Formula used
A cylinder is a three-dimensional shape with two congruent circular bases. Its volume equals base area multiplied by perpendicular height. Since the area of a circle is πr², the standard formula becomes:
When diameter is known, substitute r = d/2. When circumference is known, substitute r = C/(2π). A hollow cylinder uses the difference between the outer and inner circular areas. A partially filled horizontal cylinder requires a circular-segment calculation before multiplying by cylinder length.
| Calculation | Formula | Required values |
|---|---|---|
| Solid cylinder | V = πr²h | Radius and height |
| Using diameter | V = πd²h/4 | Diameter and height |
| Using circumference | V = C²h/(4π) | Circumference and height |
| Using base area | V = Aᵦh | Base area and height |
| Find height | h = V/(πr²) | Volume and radius |
| Find radius | r = √(V/(πh)) | Volume and height |
| Hollow material | V = πh(R² − r²) | Outer radius, inner radius, height |
| Vertical liquid | V = πr²d | Radius and liquid depth |
| Mass | m = ρV | Density and volume |
| Density | ρ = m/V | Mass and volume |
How to use this calculator
Start by choosing the calculation mode. Use the standard modes for a complete solid cylinder. Choose a reverse mode when volume is known but one dimension is missing. Select hollow cylinder for pipes, sleeves, tubes, and drilled parts. Use a fill mode for tanks that contain liquid below full capacity.
Enter each measurement and choose its unit beside the field. Measurements may use different units. For example, radius may be entered in inches while height is entered in feet. The calculator converts both values consistently before calculation.
Choose primary and secondary output volume units. Then select dimension and area units for the supporting geometry results. Set decimal places, notation, and rounding behavior. Submit the form to view volume, converted capacity, radius, diameter, circumference, surface areas, exact expressions, and calculation steps.
Use the copy button for a quick text result. Use print for a clean calculation report. Download creates a simple text record. Saved inputs and local history stay in your browser. They are not sent to a database.
Measuring a cylinder correctly
Measure the radius or diameter
Measure across the circular base through its center to obtain diameter. Divide diameter by two for radius. When the center is difficult to locate, measure circumference with a flexible tape. The calculator can derive radius directly from circumference.
Measure perpendicular height
Height must be perpendicular to the circular bases. Do not measure along a slanted outer edge. For a pipe or horizontal tank, measure its axial length. End caps, domes, and rounded shoulders are not part of a true cylinder and require separate volume formulas.
Check inside and outside measurements
For a hollow cylinder, outer radius measures the complete exterior. Inner radius measures the open void. Wall thickness equals outer radius minus inner radius. Inner radius must remain smaller than outer radius.
Use cubic units
Volume is always reported in cubic units. A cylinder measured in centimeters naturally produces cubic centimeters. Capacity units such as liters and gallons are volume units too. One milliliter equals one cubic centimeter exactly.
Worked examples
Example one: solid cylinder
A cylinder has radius 5 centimeters and height 12 centimeters. Square the radius to get 25 square centimeters. Multiply 25 by 12 to get 300 cubic centimeters. Multiply by π. The volume is approximately 942.4778 cubic centimeters.
Example two: diameter input
A storage can has diameter 20 centimeters and height 30 centimeters. Radius is 10 centimeters. The volume is π × 10² × 30. This equals approximately 9,424.778 cubic centimeters, or about 9.4248 liters.
Example three: hollow tube
A tube has outer radius 6 centimeters, inner radius 4 centimeters, and length 20 centimeters. The material cross-sectional area is π(36 − 16), or 20π square centimeters. Multiply by 20 centimeters. Material volume is 400π, or about 1,256.6371 cubic centimeters.
Example four: reverse radius
A cylinder must contain 10 liters and has height 50 centimeters. Convert 10 liters to 10,000 cubic centimeters. Radius equals the square root of 10,000 divided by 50π. The required radius is approximately 7.9788 centimeters.
Practical cylinder calculations
Cylinder volume appears in manufacturing, construction, plumbing, laboratory work, storage planning, and household projects. A water tank calculator estimates capacity before installation. A pipe calculation estimates material, internal capacity, or coating quantity. Concrete column volume helps estimate wet concrete requirements.
Machining projects use hollow-cylinder volume to estimate raw material mass. Packaging teams compare cans with different radii and heights. Laboratories estimate sample-tube capacity. Food producers calculate container fill. Farmers calculate drum and silo capacities when the shape is cylindrical.
Mass calculations require material density. Water is close to 1,000 kilograms per cubic meter under common conditions. Steel is much denser. Density depends on material, temperature, composition, and pressure. Use a reliable density value for engineering work.
Cost calculations multiply volume by a price rate. Confirm whether a supplier charges per liter, cubic foot, cubic yard, or cubic meter. Waste, shrinkage, cutting allowance, and minimum order quantities may need separate adjustments.
Frequently asked questions
What is the volume formula for a cylinder?
Volume equals π multiplied by radius squared and height: V = πr²h.
Can I use diameter instead of radius?
Yes. The calculator divides diameter by two. The equivalent formula is V = πd²h/4.
Why does the answer use cubic units?
Volume measures three-dimensional space. Length is multiplied in three dimensions, producing cubic units.
How do I calculate tank capacity in liters?
Enter the cylinder dimensions, then select liters as the primary output unit.
Does a hollow cylinder include the empty center?
No. Hollow material volume subtracts the inner void from the outer cylinder.
How is a horizontal partial fill calculated?
The calculator finds the circular-segment area created by liquid depth, then multiplies that area by cylinder length.
Can input measurements use different units?
Yes. Each relevant measurement has an independent unit selector.
Is this suitable for pressure vessels with rounded ends?
The cylindrical center section is supported. Rounded, hemispherical, ellipsoidal, or torispherical ends require additional formulas.
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Important accuracy note
This calculator is suitable for general planning and education. Verify dimensions, units, tolerances, density data, safety factors, and applicable standards before using results for structural, pressure, medical, commercial, or safety-critical decisions.