Cylinder Calculator
One cylinder, every measurement: plug in the radius and height to get volume, surface area, and more in a single click.
Cylinders are everywhere — soup cans, water tanks, pipes, candles, grain silos — and sooner or later you need their measurements. How much does that tank hold? How much paint covers that pipe?
This calculator answers all of it at once. Enter the radius and height and it returns four numbers: volume, total surface area, lateral surface area, and base area — each clearly labeled so you know exactly which one to use.
A unit selector keeps everything consistent. Pick centimeters, meters, inches, or feet, and volumes come out in cubic units while areas come out in square units.
What Does the Cylinder Calculator Do?
The calculator computes four properties of a right circular cylinder from just two inputs. Volume tells you the capacity. Total surface area covers the whole outside. Lateral surface area isolates the curved side wall. Base area gives the area of one circular end.
The headline result reads like “A cylinder with radius 3 cm and height 7 cm holds about 197.92 cubic cm.”
All four results are rounded to two decimal places, which is precise enough for DIY projects, homework, and most engineering estimates.
How to Use the Cylinder Calculator
Type the radius — the distance from the center of the circular end to its edge — into the first field.
Type the height — the straight distance between the two circular ends — into the second field.
Choose your unit, press Calculate, and read the four labeled cells. Radius and height must use the same unit, and both must be above zero.
Volume: How Much a Cylinder Holds
Volume is the capacity — how much liquid, grain, or air fits inside. It answers “how big is the tank?”
The formula is:
Volume = π × r2 × h
Square the radius, multiply by the height, multiply by π. The result is in cubic units of whatever you entered.
For a quick sanity check, compare against a box: a cylinder holds about 78.5% of the volume of the square box that encloses it.
Total Surface Area: Every Face Counted
Total surface area covers the complete outside of a closed cylinder: the curved wall plus both circular ends.
The formula is:
Total surface area = 2 × π × r × (r + h)
This is the number you need when the whole object gets painted, wrapped, or coated.
A useful cross-check: total surface area always exceeds lateral area, since the ends add positive area. If your total is smaller, something went wrong.
Lateral Surface Area: The Curved Side Only
Lateral surface area is just the curved wall — the label on a can, the pipe’s outer surface — without the top and bottom.
The formula is:
Lateral surface area = 2 × π × r × h
Use this when the ends are open or irrelevant, like a pipe carrying water or a paper towel roll.
Base Area: One Circular End
The base area is the area of a single circular face: π × r2.
It is the footprint of the cylinder — how much floor space a tank occupies.
It also appears twice inside the total surface area formula, which is why the calculator lists it separately.
If you need the material for both lids of a drum, double this cell — the calculator shows one end only.
The Four Formulas Side by Side
All four results come from the same two numbers, r and h. Volume is πr2h. Total surface area is 2πr(r + h). Lateral area is 2πrh. Base area is πr2.
Notice that volume grows with the square of the radius. Doubling the radius quadruples the capacity — a fact worth remembering when sizing containers.
Surface area grows with the square of the radius too, but only linearly with height. Tall, skinny cylinders maximize volume per unit of wall material.
The calculator’s note line repeats the two most-used formulas so you can verify the results by hand.
Radius vs Diameter: The Classic Trap
The most common error in cylinder math is entering the diameter where the radius belongs. If your tape measure gives you the width across the circle, halve it first.
A 10-inch diameter means a 5-inch radius. Using 10 as the radius would quadruple every area and volume result.
When in doubt, check: the radius should be roughly half of what you measured across the full circle.
Units: Cubic, Square, and Plain
Volume always comes out in cubic units — cm³, m³, in³, ft³. Surface areas come out in square units — cm², m², in², ft².
Keep radius and height in the same unit. Mixing centimeters with meters silently corrupts every result.
The unit selector applies to both inputs at once, which is what keeps them consistent.
Why the Calculator Rejects Zero and Negative Values
A radius or height of zero describes a flat disk or a line, not a cylinder — the formulas collapse to zero or lose meaning.
Negative lengths do not exist in the physical world, so the calculator refuses them.
If you see the red error message, check for a typo: a missing decimal point can turn 2.5 into 25 or 0.25 into 25.
Common Cylinder Calculation Mistakes
Beyond the radius-diameter mix-up, the next biggest mistake is forgetting to square the radius in the volume formula. π × r × h is wrong; π × r2 × h is right.
Another is using total surface area where only the curved side is needed — painting a pipe’s interior calls for lateral area, not total.
A third is rounding too early. Keep full precision through the calculation and round only the final answer.
A fourth is mixing up which result answers the question — grabbing volume when the job needed surface area. Always match the cell to your actual question.
Where Cylinder Calculations Are Useful
Builders size water tanks and septic systems by volume. Painters estimate coating from surface area.
Engineers compute pipe capacity and material needs. Cooks scale recipes between pans of different sizes.
Students meet cylinders in geometry class, where these four formulas are among the most-tested topics.
Aquarium owners compute water volume for dosing treatments, and bakers convert pan sizes — a 9-inch round pan and an 8-inch square pan hold surprisingly different batters.
How to Interpret Your Result Correctly
Start with the headline sentence: it confirms your inputs and gives the volume, which is the result most people want.
Then scan the four cells. Pick the one that matches your actual question — capacity, whole-coverage, side-only, or footprint.
Double-check the unit symbols: ³ for volume, ² for areas. If they look wrong, recheck that both inputs used the same unit.
Worked Example: Radius 3 cm, Height 7 cm
Inputs: radius 3 cm, height 7 cm.
First: volume = π × 32 × 7 = π × 9 × 7 = 197.92 cm³.
Then: total surface area = 2 × π × 3 × (3 + 7) = 2 × π × 3 × 10 = 188.50 cm².
Lateral area = 2 × π × 3 × 7 = 131.95 cm².
Base area = π × 9 = 28.27 cm².
Answer: this small cylinder holds 197.92 cm³ and has 188.50 cm² of total surface.
Worked Example: Radius 5 m, Height 12 m
Inputs: radius 5 m, height 12 m — think of a storage tank.
First: volume = π × 52 × 12 = π × 25 × 12 = 942.48 m³.
Then: total surface area = 2 × π × 5 × (5 + 12) = 2 × π × 5 × 17 = 534.07 m².
Lateral area = 2 × π × 5 × 12 = 376.99 m².
Base area = π × 25 = 78.54 m².
Answer: the tank holds 942.48 m³; painting the entire outside needs 534.07 m² of paint.
Worked Example: A Short Wide Cylinder
Inputs: radius 6 in, height 2 in — a squat disk shape.
First: volume = π × 62 × 2 = π × 36 × 2 = 226.19 in³.
Then: total surface area = 2 × π × 6 × (6 + 2) = 2 × π × 6 × 8 = 301.59 in².
Lateral area = 2 × π × 6 × 2 = 75.40 in².
Base area = π × 36 = 113.10 in².
Answer: 226.19 in³ of volume, with 301.59 in² of total surface — the two flat ends dominate here.
Worked Example: Checking Diameter First
Inputs: you measured a diameter of 10 ft and a height of 15 ft.
First: halve the diameter — radius = 10 ÷ 2 = 5 ft.
Then: volume = π × 52 × 15 = π × 25 × 15 = 1178.10 ft³.
Total surface area = 2 × π × 5 × (5 + 15) = 2 × π × 5 × 20 = 628.32 ft².
Lateral area = 2 × π × 5 × 15 = 471.24 ft². Base area = π × 25 = 78.54 ft².
Answer: 1178.10 ft³ capacity. Entering the diameter directly as the radius would have quadrupled every number.
Worked Example: A Small Can
Inputs: radius 2.5 in, height 9 in.
First: volume = π × 2.52 × 9 = π × 6.25 × 9 = 176.71 in³.
Then: total surface area = 2 × π × 2.5 × (2.5 + 9) = 2 × π × 2.5 × 11.5 = 180.64 in².
Lateral area = 2 × π × 2.5 × 9 = 141.37 in². Base area = π × 6.25 = 19.63 in².
Answer: 176.71 in³ of volume — about 0.77 gallons — with 180.64 in² of total surface.
Frequently Asked Questions
1. What is the difference between total and lateral surface area?
Total surface area includes the curved wall plus both circular ends. Lateral surface area is only the curved wall. For an open pipe, use lateral; for a closed tank, use total.
2. How do I find the volume of a cylinder?
Use volume = π × r² × h: square the radius, multiply by the height, multiply by π (about 3.14159). The result is in cubic units.
3. Do I enter the radius or the diameter?
The radius. If you measured across the full circle, that is the diameter — divide it by 2 before entering.
4. Can the radius and height use different units?
No. Both must be in the same unit, which the unit selector guarantees. Mixing inches with feet would corrupt every result.
5. Why does doubling the radius quadruple the volume?
Volume depends on r2, so scaling the radius by 2 scales the result by 22 = 4. Radius changes matter far more than height changes.
6. What does the base area cell tell me?
The area of one circular end, πr2. It is the cylinder’s footprint — useful for floor space or for the material of one lid.
7. Which result do I use for painting a tank?
Total surface area, since paint covers the wall and both ends. For the inside of an open-top tank, use lateral area plus one base area.
8. How accurate are the two-decimal results?
Very. The calculator uses full-precision π internally and rounds only for display. Two decimals are plenty for construction and homework.
9. What if my cylinder is hollow, like a pipe?
Treat it as two cylinders — outer and inner — and subtract the inner volume from the outer volume for the material, or add both lateral areas for total pipe surface.
10. Why does the calculator reject zero?
Zero radius or height describes a flat shape, not a cylinder. The formulas still evaluate but the results would be meaningless, so the calculator asks for a positive value.
11. What is the formula for lateral surface area?
lateral area = 2 × π × r × h. Imagine unrolling the curved wall into a rectangle: its sides are the circumference (2πr) and the height.
12. Can I use this for an elliptical cylinder?
No. These formulas assume a perfectly circular base. Elliptical cylinders need different math.
13. How do I convert cubic inches to liters?
Multiply cubic inches by 0.0163871. A cylinder holding 226.19 in³ holds about 3.71 liters.
14. Does the order of radius and height matter?
No. The formulas are symmetric in how they use the two values — swapping them changes nothing. What matters is entering the correct radius and the correct height.
15. Why are there four results instead of one?
Different questions need different numbers. Capacity, full coverage, side-only coverage, and footprint are four distinct measurements, and one input pair produces all of them.