Stopping distance calculator
Total stopping distance: reaction plus braking.
Fill in the fields and the result will appear here automatically.
Splits a conditional stopping distance into travel during reaction and braking at constant deceleration. Enter speed, reaction time, friction coefficient and longitudinal grade; positive grade means uphill. The grade correction is linear and uses a small-angle approximation. Defaults are a scenario, not guaranteed dry-road or driver properties. The model does not establish a safe following distance or replace road-design standards or testing.
How it works
Formula and logic
u = speed in km/h divided by 3.6; G = grade in % divided by 100; a = 9.80665·(μ + G) m/s². Reaction travel = u·tᵣ, braking distance = u²/(2a), total is their sum; braking time = u/a. This is a linear grade approximation, not an exact inclined-plane model. Speed and μ are positive, reaction time is nonnegative and μ + G > 0. Nonpositive a or unrepresentable outputs cause an error.
Example
At 90 km/h, reaction time 1 s, μ = 0.7 and grade 0%, the model gives 70.52 m.
Fields and units
- Speed, km/h — km/h
- Reaction time, s — s
- Friction coefficient — unitless
- Road gradient, % — %
How to use
- — Enter positive speed in km/h and nonnegative reaction time in seconds.
- — Choose positive μ for your scenario; the tool does not determine it from a surface type.
- — Enter grade as percent: uphill is positive, downhill negative.
- — Compare reaction and braking distances under the constant-deceleration and linear-grade assumptions.
Method and limitations
- Calculation method
- Formula and logic
- Data or methodology source
- OpenStax §2.5: displacement, average velocity and stopping at constant deceleration FHWA: road-design conditions and reaction time, not a standard for this model’s current inputs
- Limitation
- This is a linear grade approximation, not an exact inclined-plane model. Choose positive μ for your scenario; the tool does not determine it from a surface type.
FAQ
Why does braking distance grow quadratically?
Because the brakes dissipate kinetic energy, which goes as the square of speed. Double the speed and there is four times the energy, so at the same grip the distance is four times as long.
How dangerous is speeding?
At the same deceleration, the braking part at 120 km/h is 1.44 times its value at 100 km/h. Reaction travel grows linearly, so that multiplier does not apply to total stopping distance. Collisions or impact speed are not modelled.
How does gradient matter?
In this model uphill increases μ + G and downhill reduces it. Enter grade as percent, not degrees. When μ + G ≤ 0 the model has no positive braking deceleration and rejects the input; this is not a universal statement about a real vehicle.
Does ABS shorten the distance?
ABS, brake condition and tyres are not separate inputs. The calculator cannot predict ABS behaviour or a guaranteed shorter distance; all braking is reduced to the chosen constant deceleration.