Cylinder volume in liters
To get the cylinder volume in liters, compute V = π × r² × h with the radius and height in centimeters, then divide by 1,000, because one liter is 1,000 cm³. A cylinder 30 cm across and 50 cm tall holds π × 15² × 50 = 35,343 cm³, or 35.34 L.
Contents
Liters = π × r² × h ÷ 1,000, with r and h in centimeters. With d = 30 cm (r = 15 cm) and h = 50 cm: π × 225 × 50 = 35,343 cm³ = 35.34 L.
The calculator above accepts millimeters, centimeters, meters or inches and gives the capacity in liters, with US gallons and cubic units next to it. The same cylinder volume formula sits behind every unit; only the final conversion changes.
Why one liter is one cubic decimeter
A liter is defined as a cubic decimeter: a cube 10 cm on each side. That cube holds 10 × 10 × 10 = 1,000 cm³. One milliliter is therefore exactly one cubic centimeter, and one cubic meter holds 1,000 liters.
This gives a handy trick. If you measure the cylinder in decimeters (tenths of a meter), the formula gives liters directly, with no conversion at all. A tank 4 dm across and 6 dm tall holds π × 2² × 6 = 75.40 dm³, which is 75.40 L. The same tank in centimeters, 40 cm by 60 cm, gives 75,398 cm³ ÷ 1,000 = 75.40 L.
Liters from millimeters, centimeters and meters
| Radius and height in | Formula for liters | Diameter shortcut |
|---|---|---|
| millimeters (mm) | π × r² × h ÷ 1,000,000 | d² × h × 0.0000007854 |
| centimeters (cm) | π × r² × h ÷ 1,000 | d² × h × 0.0007854 |
| decimeters (dm) | π × r² × h | d² × h × 0.7854 |
| meters (m) | π × r² × h × 1,000 | d² × h × 785.4 |
| inches (in) | π × r² × h × 0.016387064 | d² × h × 0.012870 |
The diameter shortcuts use π ÷ 4 = 0.785398…, rounded to four figures. They are accurate enough for any practical capacity, but the full formula is just as fast with a calculator.
Worked examples in liters
A jar measured in centimeters
A glass jar is 8 cm across inside and 12 cm tall. The radius is 4 cm, the base area is π × 4² = 50.27 cm², and the volume is 50.27 × 12 = 603.19 cm³. Divide by 1,000: 0.603 L, or 603 mL.
A pipe measured in millimeters
A pipe has a 100 mm bore and is 3 m long. Put both in millimeters: r = 50 mm, h = 3,000 mm. Then V = π × 50² × 3,000 = 23,561,945 mm³. Divide by 1,000,000: 23.56 L, which is 7.854 L per meter of pipe. For gallons per foot and other pipe sizes, see the pipe volume calculator.
A tank measured in meters
A water tank is 1.2 m across and 1.5 m tall. The radius is 0.6 m, so V = π × 0.36 × 1.5 = 1.6965 m³. Multiply by 1,000: 1,696.5 L. That is 448.2 US gallons or 373.2 imperial gallons. Each meter of height holds 1,131 L.
A can measured in inches
A can is 6 in across and 10 in tall. V = π × 3² × 10 = 282.74 in³. One cubic inch is exactly 16.387064 cm³, so the can holds 282.74 × 16.387064 = 4,633 cm³ = 4.633 L, or 282.74 ÷ 231 = 1.224 US gallons. The cylinder volume in gallons guide works through the imperial units in depth.
Liters per centimeter: table of common diameters
Each row gives the capacity of one slice of the cylinder: π × (d ÷ 2)² for a height of 1 cm, 10 cm and 1 m. Multiply by the height you need. All values are inside diameters, computed with full-precision π and rounded to four significant figures.
| Inside diameter | Liters per cm | Liters per 10 cm | Liters per meter |
|---|---|---|---|
| 5 cm | 0.01963 | 0.1963 | 1.963 |
| 7.5 cm | 0.04418 | 0.4418 | 4.418 |
| 10 cm | 0.07854 | 0.7854 | 7.854 |
| 15 cm | 0.1767 | 1.767 | 17.67 |
| 20 cm | 0.3142 | 3.142 | 31.42 |
| 25 cm | 0.4909 | 4.909 | 49.09 |
| 30 cm | 0.7069 | 7.069 | 70.69 |
| 40 cm | 1.257 | 12.57 | 125.7 |
| 50 cm | 1.963 | 19.63 | 196.3 |
| 60 cm | 2.827 | 28.27 | 282.7 |
| 80 cm | 5.027 | 50.27 | 502.7 |
| 100 cm | 7.854 | 78.54 | 785.4 |
| 120 cm | 11.31 | 113.1 | 1,131 |
| 150 cm | 17.67 | 176.7 | 1,767 |
| 200 cm | 31.42 | 314.2 | 3,142 |
Notice the pattern: the 10 cm diameter gives 0.07854 L per cm and the 100 cm diameter gives 7.854 L per cm. Ten times the diameter means a hundred times the capacity, because the radius is squared.
Liters from the circumference
On a large drum or a rain barrel, wrapping a tape around the outside is easier than measuring across the middle. The circumference C is 2πr, so r = C ÷ (2π) and the volume becomes V = C² × h ÷ (4π). With centimeters, divide by 1,000 for liters.
A barrel with a circumference of 157 cm and a height of 90 cm has a radius of 157 ÷ (2π) = 24.99 cm. Its volume is 157² × 90 ÷ (4π) = 176,535 cm³, or 176.5 L. A tape around the outside includes the wall, so the true capacity is a little smaller.
Liters in a partly filled cylinder
For an upright cylinder, the liquid takes the shape of a shorter cylinder with the same radius. Use the depth of the liquid as h. A container 30 cm across holds 0.7069 L per centimeter, so 20 L of water stand 20 ÷ 0.7069 = 28.3 cm deep. Working backwards from a volume to a height is explained on the page about the height of a cylinder.
A cylinder lying on its side is different: the liquid forms a circular segment, and the liters per centimeter change with depth. The cylinder tank volume calculator handles that case.
Converting liters to other units
| From liters to | Do this |
|---|---|
| milliliters (mL) or cm³ | multiply by 1,000 |
| cubic meters (m³) | divide by 1,000 |
| US gallons | divide by 3.785411784 |
| imperial gallons | divide by 4.54609 |
| cubic feet | divide by 28.316846592 |
To express the same capacity in cubic feet and cubic yards, use the cubic feet of a cylinder calculator. Since a liter of water weighs about 1 kg, liters also give a quick weight estimate; for steel, concrete and other materials, the cylinder weight calculator multiplies the volume by the density.
Common mistakes
- Dividing by 1,000 when you measured in millimeters. Cubic millimeters must be divided by 1,000,000 to give liters. Dividing by 1,000 gives milliliters.
- Mixing centimeters and meters. A radius of 15 cm and a height of 0.5 m must become 15 cm and 50 cm (or 0.15 m and 0.5 m) before you multiply.
- Using the diameter as the radius. The 8 cm jar above would show 2.41 L instead of 0.603 L, four times too much.
- Outside measurements. Wall thickness reduces the capacity. Measure inside, or subtract twice the wall from the outside diameter.
Quick check: a cylinder 10 cm across holds about 0.79 L for every 10 cm of height. A 1 m diameter holds about 785 L per meter.
FAQ
How do you calculate the volume of a cylinder in liters?
Measure the radius and height in centimeters, compute π × r² × h to get cm³, then divide by 1,000. A cylinder with r = 10 cm and h = 30 cm holds π × 100 × 30 = 9,424.8 cm³, which is 9.42 L.
How many liters are in a cubic meter?
Exactly 1,000. A liter is one cubic decimeter (10 cm × 10 cm × 10 cm), and a cubic meter contains 10 × 10 × 10 of them.
How do I convert cm³ to liters?
Divide by 1,000. One liter is 1,000 cm³, and one milliliter is exactly one cubic centimeter, so 603 cm³ is 603 mL or 0.603 L.
How do I get liters when the cylinder is measured in millimeters?
Compute π × r² × h with r and h in millimeters, then divide by 1,000,000. A pipe with a 100 mm bore and 3,000 mm long holds 23,561,945 mm³, which is 23.56 L.
How many liters per centimeter of height does a cylinder hold?
Liters per cm = π × r² ÷ 1,000 with r in centimeters. A cylinder 30 cm across holds 0.7069 L for every centimeter of depth, so 20 L fill it to about 28.3 cm.
Related
- Cylinder volume in gallonsFind the volume of a cylinder in gallons: π × r² × h in inches ÷ 231, or in feet × 7.48052. US and imperial gallons, worked examples and a capacity chart.
- Cubic feetCubic feet of a cylinder = π × r² × h with r and h in feet. Mixed feet and inches, cubic inches ÷ 1,728, cubic yards and gallons, with a table per foot.
- How to find the volumeHow to find the volume of a cylinder: square the radius, multiply by π and the height. Worked examples in inches, feet, cm and m, plus common mistakes.
Updated October 12, 2026