Tank volume calculator for cylindrical tanks

Contents

1. The tank volume formula
2. How to measure a tank
3. Vertical cylindrical tank
4. Horizontal cylindrical tank
5. Tank capacity by diameter
6. How much room is left to fill
7. Tanks with domed or dished ends
8. Other cylinder jobs that use the same formula
9. Sizing a tank for a target capacity
10. Weight of a full tank
11. Other tank shapes
12. Common mistakes
13. FAQ

The calculator above takes the diameter, the height or length, and the liquid depth. Switch it between a vertical and a horizontal tank, and it returns the liquid volume, the full capacity, the percentage filled and the room left to fill, in gallons or liters. It also builds a depth chart you can print.

The tank volume formula

A cylindrical tank is a cylinder, so its capacity follows the cylinder volume formula: the area of the circular end multiplied by the length of the tank.

• Full tank: V = π × r² × L, or with the diameter, V = π × d² × L ÷ 4.
• Vertical tank, partly full: V = π × r² × f, where f is the liquid depth.
• Horizontal tank, partly full: V = L × [r² acos((r − f) ÷ r) − (r − f) √(2rf − f²)].

Keep every length in the same unit. Inches give cubic inches, feet give cubic feet, centimeters give cubic centimeters. Then convert with an exact factor: 231 in³ per US gallon, 7.48052 US gallons per cubic foot, 1,000 cm³ per liter. The page on cylinder volume in gallons explains each conversion and gives a table of common sizes.

How to measure a tank

1. DiameterMeasure straight across the round end, through the center. For capacity you need the inside diameter: measure from outside and subtract twice the wall thickness. On a thin steel or plastic tank the difference is small; on a concrete tank it is not.
2. Or the circumferenceOn a large tank it is easier to wrap a tape around the outside. Divide the circumference by π to get the diameter: 113 in around gives 113 ÷ π = 35.97 in.
3. Length or heightMeasure the straight part of the shell, end to end. On a vertical tank, that is from the floor of the tank to the top of the wall; on a horizontal tank, from one end to the other.
4. Liquid depthLower a clean stick or rod straight down to the bottom at the lowest point, pull it out and read the wet mark. For a horizontal tank, measure through a hole near the middle of the top, where the stick stands vertical.

Measure the depth, not the empty space above the liquid. If you measure the gap from the top (the ullage), subtract it from the diameter of a horizontal tank, or from the height of a vertical tank, to get the depth.

Vertical cylindrical tank

A standing tank is the simple case. Every inch of depth holds the same amount, because the cross-section is the same circle all the way up. The volume of liquid is just the base area times the depth, so the gauge is linear: half the height means half the volume.

Example in inches and gallons

A vertical tank measures 36 in across the inside and 60 in tall.

1. Radius: 36 ÷ 2 = 18 in.
2. Base area: π × 18² = 1,017.88 in².
3. Full volume: 1,017.88 × 60 = 61,072.6 in³.
4. Capacity: 61,072.6 ÷ 231 = 264.38 US gallons, or 1,000.8 liters.

With 40 in of liquid, the tank holds 1,017.88 × 40 ÷ 231 = 176.26 gallons (667.2 L), which is two thirds of the capacity because 40 is two thirds of 60. Each inch of depth is worth 1,017.88 ÷ 231 = 4.406 gallons.

Example in meters and liters

A tank 1.2 m across and 2 m tall: π × 0.6² × 2 = 2.2619 m³, so 2,261.9 liters when full. Filled to 0.8 m it holds π × 0.36 × 0.8 = 0.9048 m³, or 904.8 L. Each centimeter of depth is 11.31 L.

Horizontal cylindrical tank

A tank lying on its side holds exactly the same amount when full: use its length as L. The difference appears when it is partly full. The liquid surface is narrow near the bottom, widest at the middle and narrow again near the top, so equal steps of depth do not hold equal volumes. The cross-section of the liquid is a circular segment, not a smaller circle.

A horizontal tank 48 in in diameter and 96 in long holds π × 24² × 96 = 173,717.5 in³ = 752.0 US gallons (2,846.7 L) when full. At different depths:

A quarter of the depth holds less than a fifth of the volume. Reading a horizontal tank as if it were linear makes you underestimate the contents in the lower half and overestimate them in the upper half. The formula, a percentage table and more examples are on the page about the volume of a partly filled horizontal cylinder.

Tank capacity by diameter

For a quick estimate, multiply a figure from this table by the height of a vertical tank (in inches) or by the length of any tank (in feet). The values are the area of the circle converted to gallons, so they are exact for a flat-ended cylinder.

A vertical tank 48 in across and 60 in tall: 7.834 × 60 = 470.0 gallons. A horizontal tank 72 in across and 10 ft long: 211.51 × 10 = 2,115.1 gallons when full.

The per-inch and per-centimeter columns only apply to a vertical tank. On a horizontal tank, the volume per inch of depth changes with the level; that is why horizontal tanks are read with a tank dip chart that lists the volume at each depth.

How much room is left to fill

The space still available is the full capacity minus the current volume. The calculator shows it directly as « To fill ». For the 48 in × 96 in horizontal tank above, filled to 30 in, the liquid is 494.4 gallons (1,871.7 L), so a delivery of up to 257.6 gallons (975.1 L) would fill it to the brim. In practice, leave headroom: fuel and water expand when they warm up, and a tank is rarely filled to the last inch.

Tanks with domed or dished ends

The calculator treats the tank as a plain cylinder with flat ends. Many tanks have rounded heads that hold extra liquid beyond the straight shell, so a flat-end result is a lower bound for those tanks.

• Hemispherical ends. Two half-spheres of radius r make one sphere: add (4/3)πr³. For the 48 in × 96 in tank, the two ends add 57,905.8 in³, or 250.7 gallons, for a total of 1,002.7 gallons. The page on the volume of a cylinder with hemispherical ends works through it, including the partly full case.
• Shallower dished or elliptical heads. They hold less than a hemisphere, and the amount depends on the exact curve. The calculator does not estimate it. Use the capacity on the tank's data plate if there is one, or calibrate the tank by filling it in measured steps.

Measure L along the straight shell only. Including the domes in the length and then calculating as a flat cylinder overstates the volume.

Other cylinder jobs that use the same formula

The same base-area-times-length idea covers more than storage tanks:

To find how much water sits in a supply line or a filter housing, the pipe volume calculator gives gallons per foot from the inside diameter. To pour a round column, a pier or a post footing, the concrete cylinder calculator gives cubic yards and the number of bags.

Sizing a tank for a target capacity

To choose a tank size, fix one dimension and solve the formula for the other. For a 500-gallon tank 48 in across, the height is 500 × 231 ÷ (π × 24²) = 63.8 in. If the height is limited to 72 in, the diameter must be 2 × √(500 × 231 ÷ (π × 72)) = 45.2 in. Metric: a 1,000 L tank 1 m across needs a height of 1 ÷ (π × 0.5²) = 1.27 m. The height of a cylinder and radius of a cylinder pages show the rearranged formulas.

Weight of a full tank

Water is close to 1 kg per liter, or about 8.34 lb per US gallon. The 752-gallon horizontal tank therefore carries roughly 6,300 lb of water when full, before the weight of the tank itself. For other liquids, multiply the volume by their density; the cylinder weight calculator does it for water, steel and other materials.

Other tank shapes

A rectangular tank, such as most aquariums, is not a cylinder: its volume is length × width × height. In inches, divide by 231 for gallons, so a tank 48 × 13 × 21 in holds 56.7 gallons. A round aquarium or a column tank is a vertical cylinder: 24 in across and 24 in tall gives π × 12² × 24 ÷ 231 = 47.0 gallons. Either way, the water you can actually put in is less than the volume of the box, because of gravel, decorations and the gap left at the top.

Common mistakes

• Outside instead of inside diameter. The capacity uses the inside. A thick wall changes the result noticeably on small tanks; the hollow cylinder volume page separates the wall from the space inside.
• Diameter used as the radius. The result is four times too large.
• Mixed units. A diameter in inches and a length in feet must be put in the same unit before multiplying.
• Treating a horizontal tank as linear. Half the depth is half the volume, but a quarter of the depth is only 19.6 % of it.
• US and UK gallons. A US gallon is 3.785411784 L and a UK gallon is 4.54609 L. The 752 US gallon tank holds about 626 UK gallons. For metric work, see cylinder volume in liters.

Quick check: in a vertical tank, gallons per inch of depth = diameter² × 0.0034 (diameter in inches). For 36 in: 1,296 × 0.0034 = 4.41 gallons per inch, against 4.406 exactly.

FAQ

How do I figure the volume of a cylindrical tank in gallons?

Measure the inside diameter and the height (or length) in inches. Compute π × (d ÷ 2)² × height to get cubic inches, then divide by 231. A tank 36 in across and 60 in tall holds 61,072.6 in³ ÷ 231 = 264.4 US gallons.

How do I calculate how much liquid is in a partly full tank?

For a vertical tank, use the liquid depth as the height: the volume is π × r² × depth. For a horizontal tank, the liquid forms a circular segment, so you need the segment formula r² acos((r − f) ÷ r) − (r − f) √(2rf − f²), multiplied by the length. The calculator does both.

Can I use the circumference instead of the diameter?

Yes. Wrap a tape around the tank and divide the circumference by π (3.14159…) to get the diameter. A tank 113 in around is 113 ÷ π = 35.97 in across. Subtract twice the wall thickness if you need the inside diameter.

What size tank do I need for a given number of gallons?

Fix one dimension and solve for the other. For 500 US gallons in a tank 48 in across, the height is 500 × 231 ÷ (π × 24²) = 63.8 in. For 500 gallons in a tank 72 in tall, the diameter is 2 × √(500 × 231 ÷ (π × 72)) = 45.2 in.

Does the calculator include domed or dished tank ends?

No. It treats the tank as a cylinder with flat ends, using the length of the straight part. Domed ends hold extra liquid. Hemispherical ends add (4/3)πr³ for the pair; shallower dished ends hold less, and their volume depends on the exact profile.

How many liters are in a US gallon and a UK gallon?

One US gallon is 231 in³, which is 3.785411784 liters. One UK (imperial) gallon is 4.54609 liters. A tank of 752 US gallons is about 2,847 liters, or about 626 UK gallons.

Related

• Horizontal cylinderHorizontal tank volume calculator for a partly filled cylinder: segment formula, depth to volume table, and a worked 48 in × 96 in example in gallons.
• Tank dip chartMake a tank dip chart for any cylindrical tank: depth to gallons and liters, a full worked chart for a 48 in × 72 in tank, and how to read a dipstick.
• 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.

Updated October 12, 2026