Stopping Distance Calculator
Enter speed v and deceleration a to compute braking/stopping distance from d = v²/(2a). Doubling speed quadruples the distance.
Input Data
Results
At a glance:Stopping distance (braking distance) is the distance a vehicle travels from the moment braking begins until it comes to a complete stop. It is governed by uniformly decelerated motion: from v² = v₀² − 2ad with final speed v=0, initial speed v₀=v and deceleration a, the stopping distance is d = v²/(2a), where v is the speed before braking (m/s) and a the deceleration (m/s², positive). For example, at v=20 m/s (~72 km/h) and a=5 m/s², d = 20²/(2×5) = 40 m. The key safety lesson: d is proportional to v², so doubling the speed quadruples the distance (40 m → 160 m). Note the total stopping distance also includes the reaction distance (speed × reaction time, ~1-1.5 s); this calculator computes only the braking portion. Deceleration depends on tyre-road friction: ~6-8 m/s² on dry asphalt, much less on wet or icy roads.
Formula
Stopping distance: d = v²/(2a).
Scales with speed squared: double speed → 4× distance.
Total stopping distance = reaction distance + braking distance.
Speed: km/h ÷ 3.6 = m/s.
$$d = \frac{v^{2}}{2a}$$How to Use
- Enter the speed before braking v (m/s; km/h ÷ 3.6).
- Enter the braking deceleration a (m/s²; ~6-8 on dry roads).
- The calculator shows the braking distance d (excluding reaction distance).
Case Studies
Basic braking distance
Speed v=20 m/s (~72 km/h), deceleration a=5 m/s².
d = v²/(2a) = 400/(2×5) = 40 m.
Excludes the driver's reaction distance.
Double speed → 4× distance
Same a=5 m/s², speed raised from 20 to 40 m/s.
d = 40²/(2×5) = 1600/10 = 160 m.
The braking distance jumps from 40 m to 160 m — the danger of speeding.
FAQ
What is the formula for stopping distance?
From kinematics, d = v²/(2a), with v the speed before braking (m/s) and a the braking deceleration (m/s²). It excludes the driver's reaction distance.
Why does doubling speed quadruple the distance?
Because braking distance is proportional to v². Doubling v squares to 4×, so the distance becomes 4× larger — the core reason speeding is so dangerous.
Is stopping distance the same as total stopping distance?
No. Total stopping distance = reaction distance (distance covered while the driver reacts) + braking distance. This calculator only gives the braking portion.
Why is braking distance longer in rain?
On wet roads tyre-road friction drops, reducing deceleration a; since d=v²/(2a), a smaller a means a longer distance, so slow down and increase following distance in rain.
How do I convert km/h to m/s?
Divide km/h by 3.6: 72 km/h ÷ 3.6 = 20 m/s. Conversely, m/s × 3.6 = km/h.
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References
Content review: Calculatorism Science Team. Results are for reference only; please refer to the relevant authorities for the official figures.