Spike's Calculators

# Barrel Gauging - Kepler's Formula

Calculate the volume of a barrel using Johannes Kepler's formula.

The Kepler formula assumes that the barrel has the shape of two truncated cones joined by their base. Of all the historical formulas, this one underestimates the barrel's volume the most.

This calculator uses metres for measurements.

### Barrel Gauging - Kepler

Top Diameter m
Mid Diameter m
Barrel Height m
Liquid Weight-Pounds per US Gallon kg/litre

#### Results:

###### Barrel Volume and Capacity
Cubic Metres
Litres L
US Gallons gal US
Imperial Gallons gal Imperial
750 ml Bottles #
Number of Cases #
Liquid Weight kg

#### 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 = 𝝅h/12(m²+tm+t²)
where V is the volume
Pi = 3.14159265
h the height of the barrel
m is the mid barrel diameter
t is the top or bottom diameter
```
##### Example Calculation
Calculate the volume of the barrel using the above formula.
`The top diameter is 0.50metres, the mid diameter is 0.59metres, and the height of the barrel is 0.90 metres.`
```3.14159265 * 0.90 ÷ 12 * (0.59² + 0.50 * 0.59 + 0.50²) =
0.2356194490 * (0.3481 + 0.295 + 0.25) =
0.2356194490 * 0.8931 = 0.210431729919
```
```The barrel has a volume of 0.21043 cubic metres.

```
`Converting to litres;`
`1000 * 0.21043 = 210.43`
`This barrel can hold 210.42 litres.`
##### 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

```

### Barrel Gauging

Orchard and Vineyard Calculators