Tilted cylindrical tank volume

To perform the calculation, you must provide the tank size, angle, and liquid level.

Liquid level measurement

You must measure the liquid level at the middle line of the tank perpendicular to the tank's bottom. (see picture). You may measure the liquid level at any distance from one of the bases (If you do, you must enter the distance in a special parameter).
Alternatively, you may tilt the tank to make the zero liquid level at the top base; in this case, you must measure the tilt angle only.

You may find calculation details and formulas below the calculator.

Volume of liquid in tilted cylindrical tank

Cylinder length

Cylinder radius

Tilt angle (degrees)

Liquid level

Level measured near

upper base

lower base

Distance from the base

Distance between liquid level measurement place and nearest base. (0 if level is measured right near the base).

Calculation precision

Digits after the decimal point: 2

Calculate

Liquid level near upper base

 

Liquid level near lower base

 

Length of partially filled tank part

 

Length of fully filled tank part

 

Liquid volume

 

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I could not find a ready solution to calculate liquid volume in a tilted cylinder, so I derived the formula in this way:

Partially filled tilted tank volume formula

where - how the segment angle depends from the cylinder length x,
It can be derived as:

where
a - tilt angle,
h0 - liquid level at the upper base

If we substitute this expression in the formula we get:

where

If we take the integral we get the solution:

where
,

Determine tank part length filled with liquid

The above formulas are used for tilted tank volume calculation with these assumptions:

• Both bases partially filled with liquid.
• The liquid level h₀ is measured directly on the upper base.
• No part of the tank is dry or fully filled.

But the calculator accepts the liquid level measured on some distance near the upper or lower base. Some parts of the tank can be dry or fully filled.

To calculate liquid level directly on the upper base h_u use formulas:

where h_ll - liquid level measured on the distance l_l from the lower base, L_c - length of the tank

where h_lu - liquid level measured on the distance l_u from the upper base.
If the h_u is equal or above zero we assume h₀=h_u, and L_f = L_c.

Empty tank part

Otherwise, the h_u can be negative. That means some tank part is empty. In this case assume h₀=0 and calculate remained (filled) part L_f using formula:

where L_c is cylinder length.

Fully filled part

The liquid level directly on the lower base h₁ can be determined as:

If calculated h₁ value is greater than tank diameter, some part of our cylinder is fully filled with liquid. So we need to calculate fully filled part length as:

Fully filled part volume calculation is trivial see Cylinder

After these calculations you may substitute partially filled tank length and liquid level h₀ in the first section formulas to calculate partially filled tilted tank part volume.