Horizontal Tank Volume Calculator with Dipstick Chart

How to calculate the volume of a horizontal cylindrical tank

In a horizontal tank, volume does not follow height: with 18 in of liquid in a tank 48 in across and 80 in long, you have 214.7 US gallons out of 626.7, or 34%, not 37.5%. The calculation multiplies the wetted circular segment by the length, then adds the volume of dished heads. It works for heating oil, diesel, water or slurry tanks.

Circular segment formula

With R the inside radius, h the liquid height and L the straight length: V = L × [R² × acos((R − h)/R) − (R − h) × √(2Rh − h²)]. At h = 0, V = 0; at h = R, half the tank; at h = 2R, the full tank (π × R² × L).

Dished heads

Two ellipsoidal heads of depth a add π × a × h² × (1 − h/(3R)). A hemispherical head has a = R; a 2:1 elliptical head has a = D/4. The formula comes from D. Jones ("Calculating Tank Volume") and is implemented in the fluids library (V_horiz_ellipsoidal); this calculator reproduces its published example (D = 108 in, L = 156 in, a = 42 in, h = 36 in: 2,380.96 US gallons). Neutrium covers the same cases.

Worked example

• Tank 48 in inside diameter, 80 in long, flat heads, 18 in on the dipstick.
• R − h = 6 in; acos(0.25) = 1.318 rad; segment = 576 × 1.318 − 6 × √540 = 619.8 in².
• Volume = 619.8 × 80 = 49,585 in³ ÷ 231 = 214.7 US gal of 626.7 (34%); free space 412.0 gal.

Limits

The result assumes a perfectly cylindrical, level tank. Slope, wall thickness, stiffeners or dents change it, so the manufacturer's gauge chart takes precedence. For slurry storage sizing, see the manure storage calculator.

Frequently Asked Questions

How do I find how many gallons are left in a horizontal tank?

Dip a stick to the bottom, read the wetted height, then apply the circular segment formula with the inside diameter and straight length. In a tank 48 in across and 80 in long, 18 in of oil is about 214.7 US gallons, or 34% of 626.7 gallons.

Why is the fill percentage different from the height percentage?

A horizontal cylinder is wider in the middle than at the bottom. At a quarter of the diameter the tank holds only 19.6% of its volume; at half height exactly 50%; at three quarters 80.4%.

How many gallons is one inch on the dipstick?

It depends on the level. Near mid-height of a flat-head tank, one inch equals 2R × L, or 16.6 US gallons for a 48 × 80 in tank, while the first inch at the bottom holds far less. That is why a gauge chart in 1-inch steps is useful.

How much volume do dished heads add?

Two 2:1 elliptical heads (each D/4 deep) add the volume of an ellipsoid: 125.3 US gallons for a 48 in diameter. Two hemispherical heads add a full sphere, 250.7 US gallons for the same diameter.

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