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Horizontal Tank Volume Calculator

Find the volume of liquid in a horizontal cylindrical tank at any fill depth using circular-segment geometry, with results in cubic feet and gallons.

Must be between 0 and the tank diameter.

Result

470 gal

A horizontal tank 4 ft in diameter and 10 ft long, filled to 2 ft, holds about 470 gallons

Quick Answer

A horizontal tank volume calculator finds the partial fill volume using a circular-segment formula: the cross-section area of the liquid equals r² × arccos((r − h) ÷ r) − (r − h) × √(2rh − h²), then multiplied by tank length. For a 10 ft diameter, 10 ft long tank filled exactly to halfway (5 ft), the volume is 392.7 cubic feet, half its full capacity of 785.4 cubic feet. Fill depth is always measured straight up from the tank bottom along the vertical axis.

What The Horizontal Tank Volume Calculator Measures

A horizontal tank volume calculator finds the volume of liquid inside a cylindrical tank that lies on its side, at any fill depth between empty and full. This is different from a vertical tank calculator, which treats the tank's cross-section as a circle seen from above and uses simple height-times-area arithmetic. In a horizontal tank, the liquid surface cuts across the circular cross-section at varying heights, so the filled area is a circular segment, and the geometry is non-linear. The calculator uses the fill depth you enter, measured from the bottom of the tank straight up along the vertical diameter, to compute the circular-segment area at that level. It then multiplies that area by the tank length to find total liquid volume. Because of the non-linear shape, a tank that is 50 percent full by depth is exactly 50 percent full by volume, but filling from 40 to 60 percent adds more volume per inch than filling from 10 to 30 percent near the bottom. The fill-level graphic on this page shows that non-linear relationship as you adjust the fill depth.

The Math Behind Horizontal Tank Partial-Fill Volume

Partial fill volume V = L × [r² × arccos((r − h) ÷ r) − (r − h) × √(2rh − h²)]. Full tank volume V_full = π × r² × L.

  • V = L × [r² × arccos((r − h) ÷ r) − (r − h) × √(2rh − h²)].
  • V_full = π × r² × L.
  • r = radius (diameter ÷ 2), h = vertical fill depth, L = tank length.
  • 1 cubic foot = 7.48052 US gallons (exact conversion).

How To Use A Horizontal Tank Volume Calculator In 4 Steps

Inputs

  • Internal diameter of the cylindrical tank in feet.
  • Internal length along the horizontal axis in feet.
  • Depth of liquid measured from the inside bottom straight up to the surface in feet.

Steps

  1. Enter the tank's internal diameter in feet (if you know the radius, double it).
  2. Enter the tank's internal length along its horizontal axis.
  3. Enter the fill depth in feet (vertical distance from bottom straight up to liquid surface).
  4. Read the liquid volume in cubic feet and gallons (1 cu ft = 7.48052 US gallons).
  5. See the fill-level graphic to visualise how the liquid sits inside the horizontal cross-section.

Horizontal Tank Volume Example With Every Step Shown

10 ft diameter, 10 ft length, 5 ft fill depth (exactly half full)

  1. Find radius: r = 10 ÷ 2 = 5 ft.
  2. Compute arccos term: arccos((5 − 5) ÷ 5) = arccos(0) = 1.5708 radians.
  3. Compute segment area: A = 25 × 1.5708 − 0 = 39.27 sq ft.
  4. Multiply by length: V = 39.27 sq ft × 10 ft = 392.7 cu ft.

392.7 cubic feet = 2,937 US gallons (exactly half of the full-tank capacity of 785.4 cu ft / 5,875 gal).

When A Horizontal Tank Calculator Gives The Right Answer

Use this calculator when you need to know how much liquid is currently in a horizontal storage tank based on a dip measurement, or when planning fill levels for fuel oil, diesel, water, or chemical storage tanks. It is also useful for sizing pump-out schedules and calculating residual volume after partial emptying. For upright or vertical cylindrical tanks, use the Tank Volume Calculator instead; this tool is specifically for horizontal, side-lying cylinders.

For other construction calculations, visit the construction calculators hub, and check the glossary for definitions of common technical terms.

Assumptions

  • The tank is a perfect horizontal cylinder with flat end caps; no adjustment is made for hemispherical, elliptical, or domed heads.
  • Fill depth is the vertical distance from the lowest point of the internal tank bottom to the liquid surface, measured along the vertical diameter.
  • Dimensions are the internal measurements of the tank, not the external shell dimensions.
  • Results are in US gallons (1 cu ft = 7.48052 US gallons); for imperial gallons, divide cubic feet by 0.1605.

Limitations

  • Does not account for tank fittings, baffles, suction sumps, or internal structures that reduce usable volume.
  • The flat-end-cap assumption means results for tanks with domed or hemispherical heads will be slightly under the true volume.
  • Does not handle tilted or inclined tanks.
  • Dipstick readings taken at an angle are not vertical fill depth; only a vertical measurement gives a correct input for this formula.

In Practice

The single most common input error is using a dipstick reading taken at an angle as if it were a vertical fill depth. A dipstick inserted through a top port at any angle other than perfectly vertical will read a longer distance than the true vertical depth of the liquid. If your dipstick reading is taken at an angle, correct it to the vertical component before entering it here. Fill depth for this calculator is always the straight vertical distance from the bottom of the tank interior to the liquid surface, measured along the vertical diameter of the circular cross-section. The live fill-level graphic on this page shows the liquid shaded at the depth you enter, which makes it easy to verify visually that the number you have entered is reasonable.

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Horizontal Tank Volume Calculator: Common Questions

How Is a Horizontal Tank Volume Different From a Vertical Tank Volume?

A vertical tank fills linearly: each inch of added liquid adds the same volume because the cross-section stays constant. A horizontal tank does not fill linearly: the cross-section of the liquid changes shape as the level rises, being widest at the centre and narrowest near the top and bottom. The formula must use circular-segment geometry rather than simple area-times-height arithmetic, which is why a horizontal tank calculator is a separate tool from a vertical one.

What Does Fill Depth Mean for a Horizontal Tank?

Fill depth is the vertical distance from the lowest internal point of the tank floor to the liquid surface, measured straight up along the vertical axis of the circular cross-section. It is not a dipstick length at an angle or a measurement along the curved tank wall. A misread fill depth is the most common source of error in horizontal tank volume calculations.

How Do I Check If My Tank Is Exactly Half Full?

At exactly half full, the fill depth equals the tank radius (half the diameter). For a 10 ft diameter tank, half full corresponds to a 5 ft fill depth. At that point, the circular-segment area equals exactly half the circle area, so the volume is exactly half the full-tank volume. This makes the half-fill case a useful sanity check for any horizontal tank volume calculation.

Does This Calculator Work for Oval or Elliptical Tanks?

No. This calculator uses circular cross-section geometry and is correct for cylindrical tanks only. Oval or elliptical cross-sections require an ellipse-segment formula with different inputs. If your tank has an elliptical cross-section, consult the manufacturer's capacity table or use an elliptical tank volume tool designed for that geometry.

What Is the Full Volume of a Horizontal Cylinder?

The full volume of a horizontal cylinder is the same as any cylinder: V = π × r² × L. For a 10 ft diameter, 10 ft long tank, that is π × 25 × 10 = 785.4 cubic feet, or 5,875 US gallons. This is the maximum volume the calculator will return when fill depth equals the full diameter.

Sources

Last updated: . Reviewed for accuracy against the formula shown above.