Calculate the approximate volume of a barrel from the difference in diameters multiplied by the height and Pi. This calculator uses metres for measurements.

Note:

The measurements used must be of the barrel's inside dimensions.

Calculator

1. enter the top diameter in metres
2. the mid diameter in metres
3. the height of the barrel in metres

Results

1. the volume of the barrel in cubic metres
2. the barrel capacity in litres
3. the capacity in US gallons
4. the capacity in Imperial gallons
5. number of standard size bottles (750ml)
6. the number of cases from this barrel ( standard case of 12 bottles)
7. the weight of the liquid inside the barrel ( one litre = one kilogram)

Formula

This formula can be found in a publication from the "Department of Public Instruction of the Canton of Geneva", of 1913.

V = (C/2)(C/2)(22/7)H
where V is the volume
C equals m(m-t)/3
m is the mid barrel diameter
t is the top or bottom diameter
22/7 closely resembles Pi
h the height of the barrel

Example Calculation

Calculate the volume of the barrel using the above formula.

The top diameter is 0.52 metres, the mid diameter is 0.61 metres, and the height of the barrel is 0.92 metres.

First, calculate the value of C; 

0.61 - (0.61 - 0.52) ÷ 3 = 
0.61 - 0.09 ÷ 3 =  
0.61 - 0.03 = 0.58

C equals 0.58.

(0.58 ÷ 2) * (0.58 ÷ 2) * (22/7) * 0.92 = 
0.29 * 0.29 * 3.142857 * 0.92 =  0.2431691

The barrel has a volume of 0.2431691 cubic metres.

Conversions

one cubic metre (m³) = 1000000 millilitres (ml)
one cubic metre (m³) = 1000 litres (L)
one cubic metre (m³) = 264.172052358148 gallons (gal) US
one cubic metre (m³) = 219.969248299088 gallons (gal) Imperial