# Stopping Distance Calculator

> Computes the reaction (thinking) distance, braking distance and total stopping distance of a vehicle from its speed, the driver's reaction time and either a road-condition friction coefficient or a given deceleration, in metres and feet.

- Calculator id: `stopping-distance` · Category: Engineering & Automotive (`engineering`) · Tool name: `calculate_stopping_distance`
- Canonical page: https://tttkmbb.com/engineering/stopping-distance · This document: https://tttkmbb.com/engineering/stopping-distance.md · JSON definition: https://tttkmbb.com/engineering/stopping-distance.json

## Purpose

Computes the reaction (thinking) distance, braking distance and total stopping distance of a vehicle from its speed, the driver's reaction time and either a road-condition friction coefficient or a given deceleration, in metres and feet.

**Use when:** You want to know how far a car travels before it stops from a given speed on dry, wet, snowy or icy roads, or the effect of reaction time.

**Do not use when:** You need the deceleration itself from speeds and times (use acceleration), or the energy dissipated in braking (use kinetic-energy).

## Input

| Parameter | Type | Unit | Required | Description |
| --- | --- | --- | --- | --- |
| `speed_km_h` | number | km/h | required | Initial vehicle speed in km/h (mph × 1.609344). (> 0, max 500) |
| `reaction_time_s` | number | s | optional, default 1.5 | Perception–reaction time before the brakes act: 1.0–1.5 s alert driver, 2.5 s is the AASHTO road-design value. (min 0, max 10) |
| `road_condition` | enum: dry \| wet \| snow \| ice |  | optional, default "dry" | Typical tyre–road friction coefficient; overridden by friction_coefficient or deceleration_m_s2 when given. |
| `friction_coefficient` | number |  | optional | Optional custom coefficient of friction (deceleration = μ × 9.80665 m/s²). (> 0, max 1.5) |
| `deceleration_m_s2` | number | m/s² | optional | Optional braking deceleration in m/s² (e.g. 3.4 for the AASHTO design value, 8–10 for a modern car with ABS on dry road); takes precedence over friction. (> 0, max 20) |

## Output

| Field | Type | Unit | Description |
| --- | --- | --- | --- |
| `speed_m_s` | number | m/s | speed_km_h / 3.6. |
| `deceleration_m_s2` | number | m/s² | μ × g or the given deceleration. |
| `reaction_distance_m` | number | m | Distance covered at constant speed during the reaction time: v × t_r. |
| `braking_distance_m` | number | m | v² / (2 a). |
| `total_stopping_distance_m` | number | m | Reaction distance + braking distance. |
| `reaction_distance_ft` | number | ft | In feet (÷ 0.3048). |
| `braking_distance_ft` | number | ft | In feet. |
| `total_stopping_distance_ft` | number | ft | In feet. |
| `braking_time_s` | number | s | v / a. |
| `total_time_s` | number | s | reaction_time_s + braking_time_s. |

## Formula

`v = speed_km_h / 3.6; a = μ × 9.80665 (or deceleration_m_s2); reaction_distance_m = v × reaction_time_s; braking_distance_m = v² / (2 a); total = reaction + braking; braking_time_s = v / a`

Constant-deceleration model on level road; braking distance grows with the square of speed. Friction values are typical (dry asphalt 0.7, wet 0.4, snow 0.2, ice 0.1); real ABS-equipped cars on dry roads reach 0.8–1.0 g. Grade, tyre wear and brake fade are not modelled.

## Data Sources

- Wikipedia – Braking distance — https://en.wikipedia.org/wiki/Braking_distance (reference, retrieved 2026-09-24)
- Wikipedia – Stopping sight distance (AASHTO parameters) — https://en.wikipedia.org/wiki/Stopping_sight_distance (reference, retrieved 2026-09-24)
- FHWA – Speed Concepts: Informational Guide, Chapter 4 (AASHTO stopping sight distance: 2.5 s perception-reaction time, 11.2 ft/s² deceleration) — https://highways.dot.gov/safety/speed-management/speed-concepts-informational-guide/chapter-4-engineering-and-technical (government, retrieved 2026-09-24)

Data freshness: `static`. Deterministic formula with fixed constants; results never go stale. Inputs supplied by the caller determine the output.

## API

- `GET https://tttkmbb.com/api/v1/calculate/stopping-distance?speed_km_h=…`
- `POST https://tttkmbb.com/api/v1/calculate/stopping-distance` with JSON body `{"inputs": {…}}`
- Response: unified envelope (`success`, `request`, `result.values`, `result.units`, `sources`, `freshness`, `timestamp`, `next_actions`, `links`); see https://tttkmbb.com/docs/response-format.md
- Schema: https://tttkmbb.com/api/v1/calculators/stopping-distance · OpenAPI operationId `calculate_stopping_distance` in https://tttkmbb.com/openapi.json
- Authentication: none. Rate limit: fair use, see https://tttkmbb.com/docs/rate-limits.md.

## MCP

- Server: `https://tttkmbb.com/mcp` (Streamable HTTP, JSON-RPC 2.0, no auth)
- Tool:  `run_calculator` with `{"calculator_id": "stopping-distance", "inputs": {…}}`

## Example

- 100 km/h, 1.5 s reaction, dry road: inputs `{"speed_km_h":100,"reaction_time_s":1.5,"road_condition":"dry"}` → `{"speed_m_s":27.7778,"deceleration_m_s2":6.8647,"reaction_distance_m":41.67,"braking_distance_m":56.2,"total_stopping_distance_m":97.87,"total_stopping_distance_ft":321.1,"braking_time_s":4.046,"total_time_s":5.546}`
- 50 km/h, 1.0 s reaction, wet road: inputs `{"speed_km_h":50,"reaction_time_s":1,"road_condition":"wet"}` → `{"reaction_distance_m":13.89,"braking_distance_m":24.59,"total_stopping_distance_m":38.48}`

```
GET https://tttkmbb.com/api/v1/calculate/stopping-distance?speed_km_h=100&reaction_time_s=1.5&road_condition=dry
```

## Limitations

You need the deceleration itself from speeds and times (use acceleration), or the energy dissipated in braking (use kinetic-energy). Constant-deceleration model on level road; braking distance grows with the square of speed. Friction values are typical (dry asphalt 0.7, wet 0.4, snow 0.2, ice 0.1); real ABS-equipped cars on dry roads reach 0.8–1.0 g. Grade, tyre wear and brake fade are not modelled. All values are computed from the formula above; no measurement or live data is involved.

## FAQ

**Why does doubling the speed quadruple the braking distance?**

Kinetic energy grows with v², and the brakes remove it at a roughly constant force, so the distance v²/(2a) quadruples while the reaction distance only doubles.

**Which reaction time should I use?**

About 1.0–1.5 s for an alert driver expecting to brake; road designers use 2.5 s to cover most drivers in unexpected situations. Distraction or fatigue adds a second or more.

## Related

- [Speed, Distance & Time Calculator](https://tttkmbb.com/physics/speed-distance-time.md) — Uniform motion during the reaction phase.
- [Acceleration Calculator](https://tttkmbb.com/physics/acceleration.md) — Deceleration from speed change and time.
- [Kinetic Energy Calculator](https://tttkmbb.com/physics/kinetic-energy.md) — Energy the brakes must dissipate.