Calculators · Towing and loads

Road gradient and hill-climb calculator

Road signs show gradients as a percentage — rise per 100 m of horizontal distance — while engineers often work in degrees, and older signs use ratios such as 1 in 10. These calculators convert between all three and work out the force and power needed to climb a gradient at a given speed. That is why heavy vehicles and trailers slow down so much on hills.

Percentage gradient to degrees and ratio

Converts a gradient in percent into degrees, a “1 in N” ratio and the height gained per kilometre. A 100% gradient is 45°, not vertical — a common source of confusion.

Results
Angle—°Slope angle from horizontal.
Ratio—1 inHorizontal distance for each unit of rise.
Rise per km (horizontal)—Height gained over one kilometre measured horizontally.

Formula
angle = arctan(% / 100)
ratio = 100 / %

Degrees to percentage gradient

Converts a slope angle into a percentage gradient. Useful for machinery and off-road vehicles, whose maximum slope ratings are often given in degrees.

Results
Gradient—%Rise per 100 units of horizontal distance.

Formula
% = tan(angle) × 100

Force and power to climb a hill

Calculates the force needed to hold a vehicle at steady speed on a gradient, including rolling resistance, and the power that takes at the wheels. Add air drag from the drag calculator for highway speeds.

Results
Force required—Gravity component along the slope plus rolling resistance.
Power at the wheels—Force multiplied by speed.

Formula
θ = arctan(% / 100)
F = m × g × (sin θ + Crr × cos θ)
P = F × v

Worked example: a 10% mountain road

  1. A 10% gradient is arctan(0.10) = 5.7°, or 1 in 10.
  2. A 1,500 kg car needs 1,500 × 9.81 × (0.0995 + 0.012 × 0.995) = 1,639 N to hold its speed.
  3. At 60 km/h that is 1,639 × 16.7 = 27.3 kW at the wheels, before air drag.
  4. Towing a 2,000 kg caravan raises the total mass to 3,500 kg and the power to about 64 kW.

Gradient conversions

PercentDegreesRatio
5%2.9°1 in 20
8%4.6°1 in 12.5
10%5.7°1 in 10
15%8.5°1 in 6.7
20%11.3°1 in 5
100%45.0°1 in 1

Related

Towing, payload and tongue weight calculatorAerodynamic drag, rolling resistance and top speed calculatorAcceleration, 0–100 km/h and quarter-mile calculatorWheel torque, tractive force and drivetrain loss calculator

About these results

Results are theoretical estimates from standard engineering formulas. Real-world figures depend on conditions these formulas do not capture. Always follow the manufacturer's specifications for maintenance, loading and safety decisions.

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