Stopping distance

Speed, reaction time, and deceleration (or μ) — thinking distance, braking distance, and total.

Theory and problem: braking. School model without t_r: decelerated motion. Tyre friction: friction force.

Result

Enter values — the result shows up here.

How it works

Thinking distance + braking distance = stopping distance.

Stopping distance is the sum: during reaction you still roll at constant v (s_react = v·t_r), then brake s_brake = v²/(2a). Together s_total = v·t_r + v²/(2a).

Default t_r = 0.8 s (editable). Check: v = 13.9 m/s, a = 6, t_r = 0 → same as pure decelerated motion; t_r = 1 s → +13.9 m thinking distance.

Road-safety intent. School decelerated motion stays for “s and t without reaction time”.

Instead of a you can enter μ — then a = μg (g = 9.81). Related: momentum, work, friction force.

Chart: s_total vs v at your t_r and a — speed squared stands out.

How to use

Enter speed v just as the hazard appears.
Set t_r (default 0.8 s) or type your own.
Enter deceleration a > 0 or μ (then a = μg).
Read thinking distance, braking distance, total, and t_brake.
Compare with decelerated motion at t_r = 0.

Formula

s_react = v·t_r

s_brake = v²/(2a)

s_total = s_react + s_brake

t_brake = v/a; optional a = μ g

Real-life examples

City, t_r = 0

v = 13.9 m/s, a = 6, t_r = 0 — like decelerated.

City, t_r = 1 s

Same v and a, t_r = 1 → +13.9 m.

Highway

v = 36 m/s (~80 mph), a = 7, t_r = 0.8.

Wet μ

v = 20 m/s, t_r = 0.8, μ = 0.4.

Bike

v = 8 m/s, a = 3, t_r = 0.6.

Dry asphalt μ

v = 25 m/s, t_r = 1, μ = 0.7.

Slow zone

v = 8.3 m/s, a = 5, t_r = 0.8.

Hard stop

v = 22 m/s, a = 9, t_r = 0.5.

Ice μ

v = 15 m/s, t_r = 1, μ = 0.1.

Ways to use this calculator

Road-safety estimates.
Compare t_r = 0 vs realistic.
Speed effect (v² in braking distance).
Estimate from surface μ.
Bridge to decelerated motion.
Related: momentum and work while braking.
Following-distance discussions.
Unit practice for v and distance.
Chart s_total(v).

Frequently asked questions

Different from decelerated motion?

Decelerated = school, no t_r. Here = stopping distance with reaction time (road intent).

Why 0.8 s?

A typical reaction-time order of magnitude; edit for fatigue, distraction, etc.

a or μ?

Enter a directly or μ — then a = μ·9.81. If both, μ wins.

Is a positive?

Yes — enter deceleration magnitude (6, not −6).

ABS / falling μ?

Constant-a model. Reality can be worse on wet/ice.

Speed units?

Follow the label (m/s or ft/s). Convert km/h/mph or switch the header.

What is t_brake?

Braking time v/a only, without t_r. Total time ≈ t_r + t_brake.

Momentum and work?

In Related — energy and momentum climb with v.

t_r = 0?

Then s_total = s_brake like decelerated motion.

Editable g with μ?

v1 uses g = 9.81 for a = μg.

What next?

Friction force / μ, or school decelerated motion without t_r.