How to turn a percentage gradient into a fraction gradient

When working out the gradient for an incline on a model railway, your research may well uncover advice and tolerances expressed in two different ways.

A good example of this is the many articles written advising that an optimum gradient should be between 1 in 30 and 1 in 50. But then you read another article advising a gradient of between 2 and 4%, and that can be a little confusing.

Fortunately, converting the measurements is easy. Simply divide 100 by the number in a percentage gradient and that will give you the second part of its equivalent fraction gradient. (the first part is always 1).

This is how that might look for a 4% gradient: 100 divided by 4 equals 25. Therefore the equivalent fraction gradient would be 1 in 25.

This time we work out a 3% gradient: 100 divided by 3 equals 33.3. Therefore the equivalent fraction gradient would be 1 in 33, and so on.

This also works for converting gradient measurements the opposite way round. When presented with a fraction gradient, divide 100 by the last part of the fraction to find the percentage. For example, a 1 in 50 gradient would be converted by dividing 100 by 50. The answer (2) is the gradient expressed as a percentage.

Here we see a 1 in 30 gradient converted: 100 divided by 30 equals 3.3. Therefore the equivalent percentage gradient would be 3.3% (this would usually be rounded down to 3%).