Partial Volume in a Round Hopper Tank

Calculate the amount of liquid in a partially filled round hopper tank. This tank has the shape of a cylinder with a truncated cone (funnel) bottom.
This calculator uses inches for measurements.

Approximate weight of Fuel or Water

one US gallon of water = 8.34 pounds.
one US gallon of diesel fuel = 7.1 pounds
one US gallon of gas = 6 pounds

Formula

V = 0.5r²(Y-sin(Y))L+d(W-H)
where V is the volume of the cylinder
r half the tanks height
Y=2cos-¹(r-d)/d
d the depth of the liquid inside the tank
W the width of the tank
H the tanks height

V = d*𝝅/3*p²+pa+a²
where V is the volume of the funnel
d the fill height of the liquid
𝝅 = 3.14159265
p diameter @ fill height
a half the tanks'  bottom diameter

Conversions

one cubic inch (in³) = 0.000578703703703704 cubic feet (ft³)
one cubic inch (in³) = 0.000016387064 cubic metres (m³)
one cubic inch (in³) = 0.00432900432900432 gallons (gal) US
one cubic inch (in³) = 0.00360465014990905 gallons (gal) Imperial
one cubic inch (in³) = 0.016387064 litres (L)