Calculate Cylinder Volume, Capacity and Surface Area
Enter a radius, diameter or circumference and the cylinder height. You can also calculate hollow tube material, vertical tank fill or horizontal tank fill. Independent input units are converted before the geometry is solved.
Cylinder Volume Calculator
Choose a cylinder type, enter measured dimensions and select the units you want in the result. Values stay in your browser.
Cylinder volume
Calculated from unrounded measurements
Your result will appear here.
Calculated measurements
| Measurement | Formula or basis | Result |
|---|---|---|
| Enter valid measurements to see results. | ||
Calculation steps
- Choose a mode and enter the known dimensions.
Recent calculations
How to Use This Cylinder Volume Calculator
- Select the mode. Use solid for the volume enclosed by one right circular cylinder, hollow for tube material, vertical fill for an upright tank or horizontal fill for a tank lying on its side.
- Choose the circular measurement. Enter radius, diameter or circumference. Hollow mode applies the same measurement type to the outer and inner circles.
- Enter the axial dimension. This is the height of an upright cylinder or the end-to-end length of a horizontal cylinder or tube.
- Add the fill depth when needed. Measure vertical fill from the base. For a horizontal tank, measure depth upward from the lowest internal point.
- Select output units. The calculator converts each input to metres, solves with unrounded values, then converts the final volume and area.
- Add density only if you need mass. Use a reliable density for the actual material or liquid and the applicable conditions.
Use internal dimensions for usable capacity. Exterior dimensions include wall thickness and will overstate the space inside a container. For a tube, the outer and inner measurements must describe the same cross-section and the inner radius must be smaller.
What the Calculator Finds
A right circular cylinder has two parallel circular bases joined by a straight side. Its axial height is perpendicular to those bases. This tool calculates more than a single volume so you can separate geometric volume, internal capacity, material volume and liquid fill.
The optional density calculation multiplies the relevant material or liquid volume by density. It does not assume a substance. Density varies by composition, temperature, pressure, moisture and manufacturing condition, so enter a value suited to your use.
Cylinder Volume and Surface Area Formulas
Let r be radius and H be axial height. The base is a circle with area πr². Multiplying base area by height gives cylinder volume.
If you measured diameter d, use r = d/2. The equivalent volume formula is V = πd²H/4. If you measured circumference C, use r = C/(2π), giving V = C²H/(4π).
The lateral side unwraps into a rectangle. Its width is the circle circumference and its height is the cylinder height, so lateral area is 2πrH. Add one base for an open-top cylinder or two bases for a closed cylinder.
Open-top area = 2πrH + πr²
Closed area = 2πrH + 2πr²
These are ideal geometric formulas. Handles, domed ends, seams, necks, fittings, rounded corners and wall thickness require separate measurements or a shape-specific model.
Hollow Cylinder and Tube Formula
A hollow cylinder has outer radius R, inner radius r and length L. Its material cross-section is an annulus. The calculator uses the factored difference of squares, which is more stable for thin walls than subtracting two nearly equal squared radii.
Internal capacity = πr²L
Wall thickness = R - r
Material volume and capacity answer different questions. Material volume measures the solid wall material in an open tube with two flat annular ends. Internal capacity measures the empty bore. If the object has caps or a base with nonzero thickness, their material must be calculated separately because cap thickness is not inferred.
The exposed surface area shown in hollow mode includes outer curved area, inner curved area and both annular cut ends. It does not include separate caps, coatings, threads or fittings.
Partially Filled Vertical and Horizontal Cylinders
Vertical cylinder
For an upright tank, each horizontal slice has the same circular area. If liquid depth is y, filled volume is πr²y. The full capacity uses the internal height H, and fill percentage is 100y/H. This is a direct linear relationship.
Remaining volume = πr²(H - y)
Horizontal cylinder
A horizontal tank is different. Its liquid cross-section is a circular segment, so half the liquid depth does not mean half the volume. Let depth y be measured from the lowest internal point. Segment area is:
Filled volume = AL
The calculator uses a stable cap calculation near empty and near full conditions to reduce cancellation error. It also returns exact boundary results at empty, half-full and full. The model assumes level liquid, a true circular internal cross-section, flat ends and a horizontal axis.
Worked Cylinder Volume Examples
Example 1: solid cylinder
A cylinder has radius 3 cm and height 10 cm. Volume is π × 3² × 10 = 90π = 282.7433 cm³. Its base area is 28.2743 cm², lateral area is 188.4956 cm² and closed surface area is 245.0442 cm². Because 1 cm³ equals 1 mL, capacity is about 282.743 mL.
Example 2: hollow tube
A tube has outer radius 5 cm, inner radius 4 cm and length 10 cm. Material volume is π(5 - 4)(5 + 4)(10) = 90π = 282.7433 cm³. Internal capacity is π × 4² × 10 = 502.6548 cm³. With material density 7.85 g/cm³, estimated wall mass is about 2.2195 kg.
Example 3: horizontal tank fill
A horizontal tank has internal radius 1 m, length 10 m and liquid depth 0.5 m. The circular-segment area is about 0.61418485 m², so filled volume is 6.14184849 m³. Full capacity is 31.41592654 m³, making the tank about 19.5501% full. A simple height ratio would incorrectly report 25%.
Unit Conversion Guide
Length factors must be cubed for volume and squared for area. Converting 1 foot to 0.3048 metre does not mean 1 cubic foot equals 0.3048 cubic metre. The correct cubic factor is 0.3048³.
| Volume unit | Equivalent cubic metres | Useful relationship |
|---|---|---|
| 1 cubic centimetre | 0.000001 m³ | Exactly 1 millilitre |
| 1 litre | 0.001 m³ | Exactly 1 cubic decimetre |
| 1 cubic inch | 0.000016387064 m³ | Based on 1 inch = 0.0254 m |
| 1 cubic foot | 0.028316846592 m³ | Exactly 1,728 cubic inches |
| 1 US liquid gallon | 0.003785411784 m³ | Exactly 231 cubic inches |
| 1 Imperial gallon | 0.00454609 m³ | Different from the US gallon |
Keep the unit variant with the number. US liquid gallons and Imperial gallons are not interchangeable. The calculator labels them separately and rounds only the displayed result.
Measurement Accuracy and Common Mistakes
- Using diameter as radius: this makes calculated volume four times too large because radius is squared.
- Mixing units without conversion: radius in centimetres and height in metres must be normalized before multiplication.
- Using exterior dimensions for capacity: vessel walls reduce internal radius and height.
- Applying the vertical formula to a horizontal tank: horizontal fill follows circular-segment geometry.
- Confusing material and void volume: a hollow tube's wall material is not its internal capacity.
- Rounding inputs early: radius error has a doubled first-order effect on volume because radius is squared.
Measure at several points when the object is not perfectly round. Use the mean internal diameter only when that approximation fits the purpose. For commercial, engineering or safety-critical work, use calibrated instruments, applicable standards and a qualified review.
Method and Review Sources
The solid-cylinder volume and surface-area equations follow the right-cylinder formulas presented by OpenStax Contemporary Mathematics. Unit handling follows the conversion approach described by the US National Institute of Standards and Technology, including preserving precision through the calculation and rounding once at the end.
Calculations run locally in the browser. Inputs are converted to metres, square metres, cubic metres and kilograms where needed. The horizontal segment routine uses complementary empty-cap geometry above half-full and a small-cap approximation near the endpoints. Automated checks cover known examples, unit equivalence, boundary values, malformed input, thin walls, overflow and responsive layout.
Related Calculators
Frequently Asked Questions
What is the formula for the volume of a cylinder?
The volume of a right circular cylinder is V = πr²h, where r is the base radius and h is the perpendicular height or axial length. Use consistent length units before calculating.
How do I calculate cylinder volume from diameter?
Divide diameter by two to get radius, then use V = πr²h. The direct diameter form is V = πd²h/4.
Can I use circumference instead of radius?
Yes. Radius equals circumference divided by 2π. Substitution gives V = C²h/(4π), where C is base circumference.
How do I convert cylinder volume to litres?
Convert the calculated volume to cubic metres, then multiply by 1,000. One litre equals 0.001 cubic metre, and one cubic centimetre equals one millilitre.
What is the hollow cylinder volume formula?
For outer radius R, inner radius r and length L, wall material volume is π(R² - r²)L. The calculator evaluates this as π(R - r)(R + r)L for better thin-wall stability.
Is hollow cylinder material volume the same as capacity?
No. Material volume measures the solid wall. Internal capacity measures the bore or empty interior and equals πr²L when the inner radius is r.
How is a partially filled horizontal cylinder calculated?
The liquid cross-section is a circular segment. Its area is calculated from internal radius and liquid depth, then multiplied by tank length. A simple depth percentage is not accurate except at empty, half-full and full.
What is the difference between lateral, open and closed surface area?
Lateral area includes only the curved side. Open-top area adds one circular base. Closed total surface area adds both circular bases.
Which measurement units does the calculator support?
Inputs support millimetres, centimetres, metres, kilometres, inches, feet and yards. Outputs include cubic and square units, litres, millilitres, US liquid units and Imperial gallons.
How accurate is the cylinder volume calculator?
The formulas use full browser precision and round only displayed results. Real accuracy still depends on measured dimensions, correct internal or external choice, unit selection and how closely the object matches an ideal right circular cylinder.
Measurement disclaimer: This calculator provides geometric estimates for informational and planning use. It is not an engineering drawing, certified tank calibration, trade measurement, load rating or safety approval. Confirm dimensions, material properties, tolerances and applicable requirements before purchase, fabrication, dosing, transport or technical decisions.