What is my tank volume?
Pick the tank shape and type its inside measurements. The tank volume calculator shows the capacity, and the volume of liquid at the fill height you type.
- Tank capacity
- 940.03 gal
The tank holds 940.03 gal when full, and 756.25 gal at a fill height of 36 in.
- Filled volume
- 756.25 gal
- Space left
- 183.78 gal
- Percent full
- 80.4%
- Percent empty
- 19.6%
Tank capacity: 940.03 gal. The tank holds 940.03 gal when full, and 756.25 gal at a fill height of 36 in.
How full is the tank?
How to calculate
Finds the capacity of a horizontal or vertical cylinder, rectangular, capsule, or oval tank in gallons or litres, and the volume of liquid at a fill height.
Example with the default inputs (Tank shape Horizontal cylinder, Diameter 48 in, Length 120 in, Fill height 36 in): The tank holds 940.03 gal when full, and 756.25 gal at a fill height of 36 in.
Method: Capacity from the tank shape (πr²L for a cylinder, l × w × h for a box, plus 4/3 πr³ for capsule ends); a part-full round tank uses the circular segment area r²(θ − sin θ) ÷ 2.
- Dimensions are inside measurements, and the tank is level.
- A capsule has half-sphere ends as wide as its diameter; its length is the straight part only.
- Volumes show in US gallons (231 in³), or litres in Metric.
Worked examples
Each example is checked against the calculator on every build.
- Tank shape Horizontal cylinder, Diameter 48 in, Length 120 in, Fill height 36 in gives Tank capacity 940.03 gal, Filled volume 756.25 gal, Percent full 80.449889%.Source: NIST Handbook 44, Appendix C, 1 US gallon = 231 in³ (https://www.nist.gov/pml/owm/nist-handbook-44-current-edition); Weisstein, MathWorld, circular segment area (https://mathworld.wolfram.com/CircularSegment.html)
- Tank shape Vertical cylinder, Diameter 39.37 in, Height 78.74 in, Fill height 59.06 in gives Tank capacity 414.96 gal, Filled volume 311.22 gal, Percent full 75%.
- Tank shape Rectangular, Length 78.74 in, Width 39.37 in, Height 59.06 in, Fill height 29.53 in gives Tank capacity 792.52 gal, Filled volume 396.26 gal, Space left 396.26 gal, Percent full 50%.
- Tank shape Horizontal capsule, Diameter 78.74 in, Length 118.1 in, Fill height 39.37 in gives Tank capacity 3,596.32 gal, Filled volume 1,798.16 gal, Percent full 50%.
- Tank shape Vertical capsule, Diameter 78.74 in, Length 118.1 in, Fill height 157.5 in gives Tank capacity 3,596.32 gal, Filled volume 3,043.04 gal.
- Tank shape Horizontal oval (elliptical), Width 78.74 in, Height 39.37 in, Length 157.5 in, Fill height 19.69 in gives Tank capacity 1,659.84 gal, Filled volume 829.92 gal, Percent full 50%.
- Tank shape Horizontal cylinder, Diameter 39.37 in, Length 39.37 in gives Tank capacity 207.48 gal.
How it works
Every tank uses inside measurements. The radius is r = d ÷ 2, and f is the fill height: the depth of the liquid from the bottom of the tank.
Capacity (full tank)
| Shape | Capacity | Tank height (largest fill) |
|---|---|---|
| Horizontal cylinder | πr²L | d |
| Vertical cylinder | πr²h | h |
| Rectangular | L × w × h | h |
| Horizontal capsule | πr²L + 4/3 πr³ | d |
| Vertical capsule | πr²L + 4/3 πr³ | L + d |
| Horizontal oval | π × (w/2) × (h/2) × L | h |
L is the length (for a capsule, the straight part only), w the width, and h the height. A capsule's two half-sphere ends together make one sphere of diameter d. The oval is an ellipse w wide and h high, lying along its length L.
Liquid at a fill height f
- Vertical cylinder: πr²f. Rectangular: L × w × f.
- Horizontal cylinder: S(r, f) × L, where S(r, f) is the area of a circle of radius r below a level line at height f: S = r² arccos((r − f) ÷ r) − (r − f)√(2rf − f²). The calculator uses the same area in the form r²(θ − sin θ) ÷ 2, with the central angle θ = 4 arcsin √(f ÷ 2r), and above the middle it takes the whole circle minus the empty part, πr² − S(r, 2r − f). These forms keep their accuracy in a nearly empty or nearly full tank.
- Horizontal capsule: S(r, f) × L + πf²(3r − f) ÷ 3 (the cylinder part, plus a cap of height f of the sphere made by the ends).
- Vertical capsule: below the straight part (f ≤ r), a cap: πf²(3r − f) ÷ 3. In the straight part (r < f ≤ r + L): 2/3 πr³ + πr²(f − r). Above it (f > r + L): the capacity minus a cap of height (L + d − f).
- Horizontal oval: the ellipse is a circle of radius h/2 stretched across by w ÷ h, so the liquid is (w ÷ h) × S(h/2, f) × L.
The page also shows the space left (capacity − liquid), the percent full (liquid ÷ capacity × 100), and the percent empty (space left ÷ capacity × 100). Every shape here is the same upside down, so the calculator finds the space left as the liquid volume at height (tank height − fill height), which equals capacity − liquid without the rounding of a subtraction. With the fill height left empty, only the capacity shows.
Assumptions
- The tank is level and the measurements are inside measurements.
- The fill height is from 0 up to the tank height in the table. A fill height more than the tank height (by more than one part in 10¹², which allows for rounding when it is typed in another unit) gives no answer: "The fill height cannot be more than the tank's height." (for a horizontal tank: "…more than the diameter of a horizontal tank."; for a vertical capsule: "…more than the capsule's full height: the straight part plus the diameter.").
- Each length box has its own unit; the maths runs in metres and cubic metres, with 1 in = 0.0254 m exactly. Volumes show in US gallons (1 gal = 231 in³ = 3.785411784 L exactly), or litres when the site is in Metric, with 2 decimals, rounded half up on the decimal value. Percents show with 1 decimal.
Worked examples by hand
Horizontal cylinder, 48 in across, 120 in long, filled to 36 in. r = 24 in. Capacity = π × 24² × 120 = 217,146.9 in³ = 217,146.9 ÷ 231 = 940.03 gal (3.5584 m³). For the liquid, r − f = −12 in: S = 576 × arccos(−0.5) − (−12) × √(2 × 24 × 36 − 36²) = 576 × 2.0944 + 12 × 20.785 = 1,455.79 in², so the liquid is 1,455.79 × 120 = 174,694.4 in³ = 756.25 gal, which is 80.4% full.
Vertical cylinder, 1 m across, 2 m high, filled to 1.5 m. Capacity = π × 0.5² × 2 = π/2 = 1.5708 m³. Liquid = π × 0.25 × 1.5 = 3π/8 = 1.1781 m³, 75% full.
Rectangular, 2 m × 1 m × 1.5 m high, filled to 0.75 m. Capacity = 2 × 1 × 1.5 = 3 m³. Liquid = 2 × 1 × 0.75 = 1.5 m³, space left 1.5 m³, 50% full.
Horizontal capsule, 2 m across, straight part 3 m, filled to 1 m. Capacity = π × 1 × 3 + 4/3 π × 1 = 13π/3 = 13.6136 m³. Filled to the middle, the tank is exactly half full: 6.8068 m³, 50%.
Vertical capsule, 2 m across, straight part 3 m, filled to 4 m. The full height is 3 + 2 = 5 m, so the empty part at the top is a cap of height 1: π × 1² × (3 − 1) ÷ 3 = 2π/3. Liquid = 13π/3 − 2π/3 = 11π/3 = 11.5192 m³.
Horizontal oval, 2 m wide, 1 m high, 4 m long, filled to 0.5 m. Capacity = π × 1 × 0.5 × 4 = 2π = 6.2832 m³; half full at the middle, 3.1416 m³.
Other questions people ask
How do I calculate the volume of a cylindrical tank?
Multiply π by the radius squared and by the length (or height): V = πr²L. A tank 48 in across and 120 in long has r = 24 in, so V = π × 576 × 120 = 217,147 in³, which is 940.03 US gallons (231 in³ per gallon).
How do I find the volume of liquid in a horizontal tank?
The liquid fills a circular segment along the length. Its area is r² arccos((r − f) ÷ r) − (r − f)√(2rf − f²), where f is the liquid depth; multiply by the length. The same 48 × 120 in tank filled to 36 in holds 756.25 gallons, which is 80.4% of its capacity even though the depth is 75% of the diameter.
Why is a horizontal tank at half height exactly half full, but not at other heights?
The circle is widest in the middle. Below the middle each inch of depth adds less liquid than an inch near the middle, so a quarter-depth tank is only about 19.6% full. At exactly half the diameter the two halves are equal, so it is 50% full.
How do I measure a capsule tank?
Measure the diameter and the length of the straight (cylinder) part only. The two round ends together make one sphere of the same diameter, which the calculator adds: V = πr²L + 4/3 πr³.
How many litres are in a US gallon?
One US gallon is 231 cubic inches, which is exactly 3.785411784 litres. Switch the site to Metric to see the answers in litres. The UK (imperial) gallon is larger, about 4.546 litres.
What if my tank has dished or cone-shaped ends?
This calculator covers flat, half-sphere (capsule), and oval tanks. For dished heads or a cone bottom, the answer from the closest shape is only an estimate; the tank maker’s chart is the best source.
Why is my measured volume a little less than the calculator's?
The calculator uses inside measurements and a perfectly level tank. Wall thickness, fittings, a slope, or dents all reduce the real volume. Use inside measurements, or subtract twice the wall thickness from outside measurements.