Skip to content
Calcapedia
Menu
Home & Garden

Tank Volume Calculator

Find how much a tank holds and how much liquid is in it now, for upright or horizontal cylinders, box-shaped tanks and spheres.

Level: Grades 8–10

Printable worksheet

Tank Volume Calculator

Know the answer you need? Pick an input to work backward.

Inputs
Tank shape

Measured straight up from the lowest inside point. Enter the full height or diameter for a full tank.

Result

Liquid in the tank

282.01 US gal

The tank holds about 282 of its 564 US gallons (50% full).

Total capacity
564.02 US gal
Liquid in liters
1,067.52 L
Total capacity in liters
2,135.04 L
Percent full (by volume)
50%
Filled volume
37.7 ft³
Total volume
75.4 ft³

See the step-by-step solution ↓

Step-by-step solution

  1. Total volume = π × radius² × height

    π×22×6=75.398224 ft³

  2. Filled volume = π × radius² × liquid depth

    π×22×3=37.699112 ft³

  3. Convert the filled volume to liters (1 ft³ = 28.31684659 L)

    37.699112×28.31684659=1,067.519967 L

  4. Convert to US gallons (1 US gal = 3.785411784 L)

    1,067.5199673.785411784=282.008941 US gal

Test yourself

20 quick questions built from this calculator's formula: work out results, predict what happens when an input changes, and work backward from an answer. Every answer comes with the working.

What this calculator does

Find out how much liquid is in your tank right now, and how much it holds when full. Tanks for water, fuel oil, rainwater or chemicals are usually cylinders, boxes or spheres. The full capacity comes from a standard volume formula. The amount of liquid at a given depth is trickier for any tank with curved sides. For example, a cylinder lying on its side that's a quarter full by depth holds well under a quarter of its capacity. That's because the bottom of the tank is narrow.

This calculator gives both numbers. Choose the shape and the unit you measured in. Then enter the inside measurements and the depth of liquid. You'll get the volume of liquid, the total capacity, and how full the tank is by volume. Results are in US gallons and liters.

Where it's used

Why this math matters outside the classroom:

  • Heating oil. Homeowners with a horizontal oil tank turn a dipstick reading into the gallons left using the circular-segment formula.
  • Water storage. A vertical tank 4 ft across and 6 ft tall holds π × 2² × 6 ≈ 75.4 ft³, about 564 gallons.
  • Rain barrels. Gardeners size a rainwater tank by checking how many gallons a cylinder of a given diameter and height holds.
  • Spherical tanks. A spherical tank 10 ft across holds 4/3 × π × 5³ ≈ 524 ft³.
  • Stock tanks. Farmers estimate the water left in a rectangular stock tank from its length, width and the current water depth.

Grade level and standards: Grades 8–10; Common Core State Standards for Mathematics 8.G.C.9, HSG.GMD.A.3. © Copyright 2010. National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved.

How to use it

  1. Pick the tank shape: an upright cylinder, a cylinder lying on its side, a rectangular box, or a sphere.
  2. Choose the unit you measured in: feet, inches, meters or centimeters.
  3. Enter the inside measurements and the liquid depth, measured from the lowest point inside.
  4. Read the liquid volume, the full capacity and the percentage full.

What the inputs mean

Measurement unit
If you measure in feet or inches, the main result is in US gallons. If you measure in meters or centimeters, it's in liters. Both are always shown.
Inside diameter
Use the inside diameter (the distance straight across) where you can. Measuring the outside of a thick-walled tank makes its capacity look slightly bigger than it is.
Liquid depth
Measure the liquid depth straight down from the surface to the very bottom inside the tank, for example with a dipstick. For a full tank, enter the full height or diameter.

Formula and method

vertical cylinder: total = π r² H;  filled = π r² h
horizontal cylinder: total = π r² L;  filled = L × [r² × arccos((r − h) ÷ r) − (r − h) × √(2rh − h²)]
rectangular: total = L × W × H;  filled = L × W × h
sphere: total = 4/3 π r³;  filled = π h² (3r − h) ÷ 3
1 ft³ = 28.316846592 L;  1 US gallon = 3.785411784 L

Here r is the radius (half the diameter) and h is the liquid depth. H is the tank's full height, L is its length and W is its width. π (pi) is about 3.14159, √ is the square root and arccos is the inverse cosine, which turns a ratio back into an angle.

For an upright cylinder or a box, the liquid is just a shorter version of the same shape. For a cylinder on its side, look at the liquid from the end of the tank. It fills a slice of the circle below a straight line, called a circular segment. That slice's area times the tank length gives the volume. In a sphere, the liquid forms a rounded cap shape (a spherical cap).

Volumes come out in cubic units of whatever you measured in. They're converted to liters with exact factors (1 in = 2.54 cm, 1 ft = 0.3048 m), then to US gallons.

Worked example

A horizontal cylindrical tank is 4 ft across (its diameter) and 8 ft long, with 1 ft of liquid in it.

  1. Radius: 4 ÷ 2 = 2 ft. Total volume: π × 2² × 8 = 100.53 ft³, or 752.02 US gallons.
  2. Segment area: 2² × arccos((2 − 1) ÷ 2) − (2 − 1) × √(2 × 2 × 1 − 1²) = 4.1888 − 1.7321 = 2.4567 ft².
  3. Liquid volume: 2.4567 × 8 = 19.654 ft³.
  4. Liters: 19.654 × 28.316846592 = 556.54 L; gallons: 556.54 ÷ 3.785411784 = 147.02 US gal.

Result: The tank holds about 147.02 US gallons of its 752.02-gallon capacity. So it's about 19.6% full, even though the depth is a quarter of the diameter.

Understanding the result

For upright cylinders and boxes, the percentage full by volume equals the percentage full by depth. For horizontal cylinders and spheres it doesn't. The first and last parts of the depth hold little liquid, and the middle holds the most.

The total capacity is the filled-to-the-brim figure. Tanks are normally filled to less than that, to leave room for the liquid to expand and for venting.

Assumptions and limitations

  • The inside of the tank is a perfect cylinder, box or sphere.
  • A horizontal tank is level, so the liquid depth is the same along its length.
  • Measurements are taken on the inside.
  • Domed, dish-shaped or cone-shaped ends on horizontal and upright tanks aren't included. Their extra volume is ignored.
  • A tank that sits on a slope will give a misleading depth reading.
  • Fittings and baffles (inside walls that slow sloshing) and the wall thickness reduce the real capacity slightly.

Frequently asked questions

Why is a horizontal tank half full at half its diameter, but not a quarter full at a quarter?

A circle is the same above and below its middle, so the liquid below the center line is exactly half. Below that, the circle narrows quickly. So the bottom quarter of the depth holds only about 19.6% of the volume.

How many gallons are in a cubic foot?

About 7.48 US gallons. A US gallon is exactly 231 cubic inches, and a cubic foot is 1,728 cubic inches.

How do I measure the liquid depth?

Lower a clean stick or a gauge rod straight down to the lowest point of the tank, and read the wet mark. For sealed tanks, a sight glass or a level gauge does the same job.

Can I use this for a tank with rounded ends?

Use the straight, cylinder-shaped length to get a slightly low estimate. Or use the overall length to get a slightly high one. Dish-shaped ends add a modest amount of volume that this calculator doesn't model.

How this calculator is checked

Method: Standard solid-geometry formulas: cylinder, rectangular prism, sphere, circular segment area r²·arccos((r−h)/r) − (r−h)·√(2rh−h²), and spherical cap πh²(3r−h)/3. The calculation is covered by automated tests with known reference values and edge cases. Last updated 2026-10-18. Found a problem? Tell us.

Embed this calculator

Put this Tank Volume Calculator on your own website or blog for free. Paste this code where you want it to appear: