Stopping Distance on Snow and Ice Calculator

For road grade $G$ entered as a percentage, $\theta=\arctan(G/100)$; positive is uphill. Convert speed explicitly to m/s and take $g=9.81\,\mathrm{m/s^2}$.

For each endpoint and midpoint of the selected friction range, the available friction force is $\mu m g\cos\theta$. Uphill gravity adds $m g\sin\theta$, giving

Mass cancels. The steps use the equivalent factored form $a=g\cos\theta(\mu+G/100)$ to avoid cancellation at the downhill limit. Distances follow the road surface. The exact trigonometric grade correction replaces the small-angle $g(\mu+G/100)$ approximation. Braking must have $a>0$ across the complete range. The upper friction gives the shorter stop; the lower friction gives the longer stop. Midpoint results use the arithmetic midpoint of friction, not of the distance bounds.

VTI 911A, printed p.37 (PDF p.37), supplies general surface ranges: dry 0.8–1.0, wet 0.7–0.8, packed snow 0.20–0.30, black ice 0.15–0.30, wet black ice 0.05–0.10. These are 17% slip instrument measurements and are used as illustrative effective grip.

Tire presets infer $\mu_{eff}=v_{test}^2/(2g d_{test})$ from Tire Rack's 2026 snow tests and 2008/2026 ice tests. The grip table records distances, models and test speeds. Bounds cover the included examples only. They are not a calibrated conversion from VTI equipment readings.

ABS/controlled mode uses factor 1. Locked-wheel mode multiplies both coefficients by the user-entered retained-grip fraction. The default 0.75 is an assumption. WorkSafe describes losses of up to 50% after lockup; that observation does not establish one factor for all surfaces.

Animation uses $u=\operatorname{clamp}(t-t_r,0,v_0/a)$ and $x=v_0\min(t,t_r)+v_0u-au^2/2$. Speed stays constant during reaction, decreases linearly during braking and remains zero after stopping. One playback sequence spans the longer midpoint stopping time; it does not recompute the speed sweep each frame.

• A straight road with constant grade and uniform friction; both cars have the same speed, perception/reaction time and braking mode.
• Constant speed during reaction and immediate full braking afterward. No separate brake-pressure buildup.
• Friction-limited braking with adequate brake capacity and all tires on the same surface. The model omits drag, rolling resistance and load-sensitive tire behavior.
• Tire-test presets represent only the named test examples. The snow bounds use two 2026 tire models per class; ice bounds combine separate 2008 and 2026 tests. Their narrow spans do not represent all tires or all weather.
• A tested effective coefficient already includes that test vehicle's braking-system behavior. Do not apply a second loss to measured locked-wheel data; use retained grip 1 if the coefficient already includes it.
• Range endpoints hold other inputs fixed. Reaction-time uncertainty is explored by changing its input, not included automatically in the friction envelope.

Use for comparative estimates within 1–130 km/h, reaction times 0–5 s and grades −15% to +15%, with a positive deceleration throughout both selected friction ranges. These input limits are interface limits, not validated vehicle operating limits. The tire tests were at 25 mph on snow and 10–12 mph on ice; higher-speed estimates and chart sections extrapolate speed-independent friction. Changing weather, wear, ice temperature and polishing can put actual grip outside the listed bounds.

VTI's general wet-road 0.7–0.8 range does not represent every wet pavement. FHWA's worked examples use a deliberately different design coefficient of 0.35; reproduce it with car A's measured-range option. It is not a snow coefficient.

ABS principally maintains wheel rotation and steerability; it does not guarantee a shorter stop. NHTSA documents different behavior on loose surfaces. Deep/loose snow, gravel, snow wedges, aquaplaning, mixed left/right friction, cornering and stability are outside this model. No temperature-only grip correction is applied.

These results are not a safe following-distance prescription, certified stopping sight distance, crash reconstruction or heavy-vehicle stopping assessment. The lower friction bound is not a guaranteed worst case. Conditions requiring nonpositive deceleration have no finite full-range stopping distance in this model.