Two distances, and only one of them involves the brakes
A stop is the sum of two things that behave completely differently. The first is reaction distance: the vehicle travels at its original speed for however long it takes the driver to perceive the hazard and get on the brakes. That distance is speed times time, a straight line relationship, and the road surface has nothing to do with it. At 55 mph, 1.5 seconds of reaction is 121 feet before anything has begun to slow down.
The second is braking distance, and it is where the surface lives. Kinetic energy is proportional to the square of speed and the braking force available is the friction coefficient times weight, so the distance works out as speed squared divided by twice the deceleration, where the deceleration is the friction coefficient times gravity. Both of the awkward properties are in that expression: the square on speed, and the coefficient in the denominator.
What the numbers actually do
Take 60 mph with a 1.5 second reaction. On dry pavement at a friction coefficient of 0.7 the braking distance is about 172 feet, and 132 feet of reaction distance makes 304 feet in total. On ice at 0.1 the braking distance alone is about 1,203 feet, and the total is roughly 1,335 feet. The braking part went up by a factor of seven, exactly the ratio of the two coefficients, because that term is linear in grip.
The total only went up by about four and a half times, because the reaction distance is identical in both cases and dilutes the ratio. That is worth sitting with: the reaction component is a fixed cost that no amount of grip changes, and on a good surface it is a large share of the whole stop.
| Surface | Typical coefficient | Braking distance from 60 mph | Against dry |
|---|---|---|---|
| Dry pavement | 0.70 | about 172 ft | 1x |
| Wet pavement | 0.50 | about 241 ft | 1.4x |
| Slush or loose snow | 0.30 | about 401 ft | 2.3x |
| Packed snow | 0.20 | about 602 ft | 3.5x |
| Ice | 0.10 | about 1,203 ft | 7x |
| Wet ice near freezing | 0.05 | about 2,407 ft | 14x |
Those coefficients are representative values used to demonstrate the relationship. They are not measurements of any particular vehicle on any particular road, and the real figure on a real surface moves around continuously.
Speed does more than it looks like it should
Because the braking term is squared, a proportional change in speed produces a much larger change in distance. Going from 60 to 40 mph is a third off the speed and takes the braking distance down by more than half. Going from 60 to 70 adds a sixth to the speed and adds more than a third to the braking distance. This is the reason a modest reduction in winter conditions is worth so much more than it feels like from behind the wheel, where the sensation of speed changes hardly at all.
The same squaring works against you in a way that gets underappreciated. If a stop is going to be too long, the vehicle does not merely arrive later; it arrives still moving. The calculator reports the speed you would still be carrying at the point where a dry-pavement stop would have finished, and on low grip that residual speed is frequently most of the original.
Grip is not a property of the road
The friction coefficient is a property of the interaction between a particular tyre, in its particular condition and at its particular temperature and pressure, and a particular surface, at that moment. It is not a constant of the road, and it is not a constant across a journey. A single stretch can go from wet pavement to black ice to packed snow inside a few hundred metres, and the coefficient in the shade of a bridge deck is not the coefficient in the sun a hundred metres earlier.
The specific trap in the list above is wet ice near freezing. Ice at 25 degrees offers considerably more grip than ice at 31, because as ice approaches its melting point a liquid film forms on the surface and lubricates it. The most slippery conditions therefore occur at temperatures that feel the least alarming, and they occur during a thaw as readily as during a freeze.
Because none of this is knowable in advance, the number this page produces cannot be a target. It is an argument. What it argues for is a gap large enough that you are not depending on knowing the coefficient, and a speed low enough that the squared term is not doing so much work.
What the page deliberately does not say
It states no law. Speed limits, following distance requirements, winter tyre and chain rules and any other traffic regulation are set by the jurisdiction you are in, differ between neighbouring places, and change seasonally. None of them appear here, and no distance printed by this calculator should be read as implying that a particular speed or gap is permitted, adequate or safe anywhere.
It also does not model your vehicle. Anti-lock braking, stability control, brake condition, tyre compound and tread depth, load and weight distribution all matter and none of them are inputs. What is here is the underlying relationship, and the relationship is enough to make the point that the surface term is multiplicative and the reaction term is not. The winter driving checklist covers preparation, the roadside emergency guide covers what happens if it goes wrong anyway, and the tyre size comparison is there if a change of wheel and tyre package is in the plan.
Questions people ask
What is the formula for stopping distance?
Total stopping distance is reaction distance plus braking distance. Reaction distance is speed multiplied by reaction time. Braking distance is speed squared divided by twice the deceleration, where deceleration is the friction coefficient multiplied by gravitational acceleration. On a gradient the deceleration term becomes gravity times the friction coefficient times the cosine of the slope angle, plus or minus gravity times the sine of it, with a downgrade subtracting. Everything on this page comes out of those two expressions and a table of representative coefficients.
How much longer does it take to stop on ice?
The braking portion scales inversely with the friction coefficient, so going from a dry-pavement figure around 0.7 to an icy one around 0.1 multiplies the braking distance by about seven. From 60 mph that is roughly 172 feet becoming roughly 1,203 feet. The total including reaction distance rises by less, around four and a half times, because the reaction distance is unchanged and dilutes the ratio. Both numbers depend on coefficients that are representative rather than measured, and the real ones on a real road vary continuously.
Is a three second following distance enough in winter?
This page does not offer a rule and will not, because following distance requirements are set by jurisdiction and because any single number would be wrong somewhere. What it does is let you check the arithmetic yourself: enter your speed, the surface, your reaction time and the gap you keep, and see the gap in feet against the stopping distance in feet. One thing to hold in mind when reading it is that the comparison shown is against a stationary object. A vehicle ahead that is also braking is a gentler case, and one that has already stopped, or has hit something, is not.
Why is ice near freezing more slippery than colder ice?
Because a thin film of liquid water forms on the surface as ice approaches its melting point, and that film acts as a lubricant between the tyre and the solid ice underneath. At lower temperatures the surface is drier and the effective friction is noticeably higher. The practical consequence runs against intuition: the most treacherous conditions occur at temperatures around freezing rather than well below, they occur during thaws as readily as during freezes, and they occur on bridge decks and shaded stretches while the surrounding road appears merely wet.
Do winter tyres change these numbers?
They change the friction coefficient, which is the input rather than the output, so the way to explore it is to run the calculator twice at different coefficients and compare. What this page will not do is tell you what coefficient any particular tyre achieves on any particular surface, because that depends on the compound, the tread, its depth and age, the inflation, the temperature and the exact state of the ice or snow, and published test figures are specific to the conditions of the test. Nor does this page state any legal requirement about tyres or chains, since those are set locally and change by season and by road.