Gradient Resistance Calculator

Gravity Is Always Working Against (or With) the Train

Every incline a train climbs adds a resisting force that a locomotive has to overcome on top of rolling and air resistance, and every descent hands that same force back as extra momentum the brakes have to absorb. Because a fully loaded freight train can weigh many thousands of tonnes, even a shallow grade translates into a substantial force — this calculator converts a gradient percentage and train mass directly into that force.

The Formula

Mass is converted from tonnes to kilograms, and g (9.81 m/s²) is standard gravitational acceleration. The result in newtons is also expressed in kilonewtons and as an equivalent force per tonne of train mass, which is a common way traction engineers compare gradients independent of train size.

Where This Is Useful

• Locomotive sizing — the tractive effort a locomotive must supply on a ruling grade has to exceed gradient resistance plus rolling and air resistance combined.
• Route planning — comparing gradient resistance across alternative routes helps identify which alignment needs less locomotive power or a lighter train consist.
• Braking on descents — on the way down the same grade, this force adds to the braking effort required to hold a safe speed.

Worked Example

A 500-tonne train on a 2% gradient:

The per-tonne figure follows directly from the gradient itself — a 2% grade always works out to 20 kgf of resistance per tonne of train mass, regardless of how heavy the train is.

How to Use This Calculator

1. Enter Train Mass in tonnes.
2. Enter the Track Gradient as a percentage.
3. Select Calculate to get the gradient resistance force in newtons, kilonewtons, and per-tonne terms.

Related Calculations

Combine gradient resistance with the Braking Distance Calculator to see how much further a train needs to stop on a descent, or check Axle Load to confirm the same train mass stays within track limits.