Round Tank Volume Calculator: Gallons & Liters

This round tank volume calculator works out the capacity of a horizontal or vertical cylindrical tank in gallons, liters, and cubic feet. You enter the tank diameter, length (or height for a vertical tank), and liquid depth, and it returns the total volume and the volume of liquid currently in the tank. The calculator uses the standard cylinder volume formula and the segment-area formula for partial fills, so you get an accurate answer whether the tank is full or only partly filled.

Formula

The total volume of a cylindrical tank is the area of the circular end times the length (or height):

V = π × (d/2)² × L

• V = total volume (cubic feet, then converted to gallons or liters)
• d = inside diameter of the tank (ft)
• L = length of the tank for horizontal orientation, or height for vertical orientation (ft)
• π ≈ 3.14159

To convert cubic feet to U.S. gallons, multiply by 7.48052. To convert to liters, multiply cubic feet by 28.3168.

For a partially filled horizontal tank (liquid depth < diameter), the liquid volume is the area of the circular segment (the shaded part of the circle) times the length:

V_liquid = (d²/4) × L × [cos⁻¹(1 − 2h/d) − (1 − 2h/d) × √(4h/d − 4(h/d)²)]

• h = liquid depth from the bottom of the tank (ft)
• All angles in radians
• This formula works for any fill level from 0 to d; if h = d, it simplifies to the full cylinder volume.

Worked Example

Using the default values: diameter = 4 ft, length = 10 ft, liquid depth = 2 ft.

Step 1: Total volume

Radius = 4/2 = 2 ft. Area of circular end = π × (2)² = 12.5664 ft². Multiply by length: 12.5664 × 10 = 125.664 ft³. Convert to gallons: 125.664 × 7.48052 = 940.0 gallons (rounded to 1 decimal).

Step 2: Liquid volume (partial fill)

h/d = 2/4 = 0.5. Then 1 − 2h/d = 1 − 1 = 0. cos⁻¹(0) = π/2 ≈ 1.5708. The term (1 − 2h/d) × √(4h/d − 4(h/d)²) = 0 × √(2 − 1) = 0. So the bracket = 1.5708. Multiply by (d²/4) × L = (16/4) × 10 = 40. So liquid volume = 40 × 1.5708 = 62.832 ft³. Convert to gallons: 62.832 × 7.48052 = 470.0 gallons.

Notice that at half depth, the liquid volume is exactly half the total volume (470 / 940 = 0.5). This is a good sanity check.

When to Use This Calculator

You need this calculator whenever you have a cylindrical tank that is lying on its side (horizontal) or standing upright (vertical) and you want to know:

• How much liquid it can hold when full (for sizing a new tank, checking a fuel tank, or planning water storage).
• How much liquid is currently inside based on a dipstick or level sensor reading.
• How many gallons or liters you need to fill it from empty to a certain depth.

The calculator is commonly used for:

• Home heating oil tanks (often horizontal cylinders).
• Propane tanks (though those are usually spheroids, not perfect cylinders – see limits).
• Water storage tanks, both horizontal and vertical.
• Aquariums and fish tanks (if they are cylindrical).
• Industrial chemical or food storage tanks.

How to Read the Results

The first output, Total volume, is the full capacity of the tank in U.S. gallons. The second output, Liquid volume, is the amount currently in the tank based on the depth you entered. The third output is the total volume in cubic feet, which is useful if you need to work in imperial units without gallons.

If you need liters, multiply the gallons by 3.78541. For imperial gallons (used in the UK and some Commonwealth countries), multiply U.S. gallons by 0.832674. The calculator uses U.S. gallons as the default because that is the most common in the United States.

Common Mistakes and Unit Mix-Ups

Here are the most frequent errors people make when calculating tank volume:

• Using outside diameter instead of inside diameter. The formula assumes the inside dimensions. If you measure the outside, subtract the wall thickness twice (once for each side). For a metal tank with 1/4-inch walls, that is 0.5 inches total.
• Mixing feet and inches. If you measure diameter in feet and length in inches, the result is wrong. Convert everything to the same unit first. For example, 6 inches = 0.5 feet.
• Forgetting that depth is measured from the bottom, not from the top. If you measure the empty space at the top (ullage), subtract that from the diameter to get the liquid depth.
• Using the formula for a vertical tank on a horizontal tank. The partial-fill formula is different for horizontal tanks because the cross-section is a segment of a circle, not a simple circle.
• Rounding too early. Keep at least 4 significant figures during intermediate steps, then round the final answer.

Limitations of the Formula

This calculator assumes a perfect right circular cylinder with flat ends. Real tanks often have dished or elliptical heads (ends), which add a small amount of volume. For most practical purposes, the cylinder formula is accurate to within a few percent. If you need exact capacity for a tank with curved ends, you must add the volume of the heads, which depends on their shape (hemispherical, elliptical, torispherical).

Also, the formula assumes the tank is level. If the tank is tilted, the liquid surface is not parallel to the tank axis, and the segment formula no longer applies. For a tilted tank, you need a more complex integration.

Finally, the liquid depth measurement must be taken at the lowest point of the tank (for a horizontal tank, that is the bottom center). If you measure depth at a location where the tank curves, you will get an error.

Practical Tips for Measuring

To get accurate results, follow these measuring guidelines:

• Use a tape measure that reads to at least 1/8 inch (3 mm).
• For the diameter, measure across the center of the tank end. If the tank is horizontal, measure the inside diameter at the end opening if possible.
• For the length, measure the inside length from the inside of one head to the inside of the other. If you cannot access the inside, measure the outside length and subtract the head thickness.
• For liquid depth, use a dipstick or a level sensor. If the tank is pressurized, never open it to measure – use a sight glass or ultrasonic sensor.

Frequently Asked Questions

How do I calculate the volume of a round tank in liters?

First calculate the volume in cubic feet using the formula V = π × (d/2)² × L, then multiply by 28.3168 to get liters. For example, a 4-ft diameter, 10-ft long tank has 125.664 ft³ × 28.3168 = 3558.6 liters. Alternatively, calculate gallons and multiply by 3.78541.

What is the formula for a horizontal cylinder tank with elliptical heads?

For a horizontal cylinder with elliptical heads, the total volume is the cylinder volume plus the volume of the two heads. The head volume depends on the head shape. For a 2:1 elliptical head, the volume of one head is (π/6) × d³. For a hemispherical head, it is (π/12) × d³. Add these to the cylinder volume. The liquid volume calculation becomes more complex because the heads also contain liquid; you need to integrate the segment area along the head profile.

Can I use this calculator for a vertical cylindrical tank?

Yes. For a vertical tank, the total volume is the same formula: V = π × (d/2)² × H, where H is the height. For a partial fill, the liquid volume is simply the area of the circular base times the liquid height, because the cross-section is constant. That is: V_liquid = π × (d/2)² × h. The calculator above uses the horizontal partial-fill formula, which also works for vertical tanks when h ≤ d, but it is more complicated than needed. For a vertical tank, you can just use the total volume formula and multiply by the fraction of height filled.

Why is my dipstick reading not matching the calculated volume?

There are several possible reasons: the tank may have dished heads (which add volume at the ends), the tank may be tilted, the dipstick may be calibrated for a different tank, or the dipstick may not be inserted vertically at the lowest point. Also, if the tank is not perfectly cylindrical (e.g., it has a slight bulge), the formula will be off. Re-measure the tank dimensions and check the dipstick calibration.

How many gallons are in a 1000-gallon round tank that is half full?

If the tank is a perfect cylinder and half full by depth, then the liquid volume is exactly half of the total volume, so 500 gallons. However, if the tank has dished ends, the half-full volume may be slightly more than half because the heads are not fully filled at the half-depth point. For a typical 1000-gallon tank with 2:1 elliptical heads, the half-full volume is about 505-510 gallons, depending on the head dimensions.

What is the difference between U.S. gallons and imperial gallons?

A U.S. gallon is 231 cubic inches, while an imperial gallon is 277.42 cubic inches. Therefore, 1 U.S. gallon = 0.832674 imperial gallons, and 1 imperial gallon = 1.20095 U.S. gallons. To convert from U.S. gallons to imperial, multiply by 0.832674. This calculator outputs U.S. gallons, so if you need imperial gallons, apply that conversion.

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in d | Tank diameter | ft | 4 | 0
in L | Tank length/height | ft | 10 | 0
in h | Liquid depth | ft | 2 | 0
out vol_total | Total volume | gal | pi * (d/2)^2 * L * 7.48052 | 1
out vol_liquid | Liquid volume | gal | (d^2 * L * (acos(1 - 2*h/d) - (1 - 2*h/d) * sqrt(4*h/d - 4*(h/d)^2)) / 4) * 7.48052 | 1
out vol_cuft | Total volume | cu ft | pi * (d/2)^2 * L | 2