How do you calculate a hill's gradient?
Divide the height gained by the distance traveled and multiply by 100: climb 450 feet over 1.2 miles (6,336 ft) and the grade is 450 ÷ 6,336 × 100 = 7.1%. That's the number on every climb sign, Strava segment and race profile. Degrees are a different ruler for the same slope — 7.1% is only 4.1° — which is why a grade that sounds gentle in degrees can be a wall in practice.
Percent grade to degrees: the conversion chart
Every road sign uses percent, every protractor uses degrees, and the two only line up at zero. Percent is rise over run, times 100; degrees is the arctangent of that same ratio. The chart also shows what each grade adds up to over a mile or a kilometer of road — the number you actually feel.
| Grade | Degrees | Gain per mile | Gain per km |
|---|---|---|---|
| 1% | 0.6° | 53 ft | 10 m |
| 2% | 1.1° | 106 ft | 20 m |
| 3% | 1.7° | 158 ft | 30 m |
| 4% | 2.3° | 211 ft | 40 m |
| 5% | 2.9° | 264 ft | 50 m |
| 6% | 3.4° | 316 ft | 60 m |
| 8% | 4.6° | 421 ft | 80 m |
| 10% | 5.7° | 525 ft | 100 m |
| 12% | 6.8° | 629 ft | 119 m |
| 15% | 8.5° | 783 ft | 148 m |
| 20% | 11.3° | 1035 ft | 196 m |
| 25% | 14.0° | 1281 ft | 243 m |
| 30% | 16.7° | 1517 ft | 287 m |
Degrees = arctan(grade ÷ 100). Gain is along a mile (or km) of road, computed by the same engine that derives our climb presets; it differs from "rise per horizontal mile" by under 1% until 15%.
What does each gradient feel like?
Adjectives lie, so here are speeds instead — the same 200 W rider, computed by the physics engine behind our power ↔ speed calculator:
| Grade | Degrees | Speed at 200 W | From the saddle |
|---|---|---|---|
| 3% | 1.7° | 12.7 mph | Big-ring climbing — a false flat with opinions |
| 6% | 3.4° | 8.0 mph | Honest climbing; conversation gets short |
| 9% | 5.1° | 5.6 mph | Low gear, out of the saddle in surges |
| 12% | 6.8° | 4.3 mph | Every pedal stroke is a decision |
| 15% | 8.5° | 3.5 mph | Paperboy zig-zags start looking rational |
165 lb rider + 19 lb bike, steady 200 W, paved road. Time up a specific climb — including the famous ones — is the climb time calculator's job.
How much slower does each percent make you?
This is the question hiding behind "is 6% steep?", and it has a computed answer. The same 165 lb rider, holding a steady 200 W:
| Grade | Speed at 200 W | Minutes per mile | Watts to hold 10 mph |
|---|---|---|---|
| 0% | 20.9 mph | 2:52 | 35 W |
| 2% | 15.1 mph | 3:58 | 109 W |
| 4% | 10.7 mph | 5:36 | 184 W |
| 6% | 8.0 mph | 7:33 | 258 W |
| 8% | 6.2 mph | 9:38 | 332 W |
| 10% | 5.1 mph | 11:46 | 406 W |
| 12% | 4.3 mph | 13:56 | 479 W |
165 lb rider + 19 lb bike, still air, on the hoods — the Martin power model. Below about 4% the air is still your main opponent; above it, gravity takes over.
Read the middle column as time: the same mile takes 2:52 on the flat and 9:38 at 8% — 3.4× longer for the same watts. Turn the last column around and you can see why "just hold 10 mph" stops being a plan on anything over 6%: at 8% it asks for 332 W, which is at or beyond most riders' threshold. The power ↔ speed calculator runs this at your own watts and weight, and the VAM calculator turns a climb time back into the W/kg it took.
A 100% grade isn't a vertical wall — it's 45°, rising one foot for every foot forward. Road signs and cycling always use percent; degrees mostly appear when someone wants a small number to sound scarier or a big one to sound tamer. The steepest paved public roads on Earth top out around 35% (about 19°), and even those are short bursts, not climbs.
What counts as a steep climb?
Useful anchors from the sport: highway engineers start adding runaway truck ramps around 6–7%; Tour de France categorized climbs mostly average 5–9%, with the legendary ones (Alpe d'Huez 8.1%, the Angliru averaging 9.8% with ramps over 23%) earning their reputations by holding those numbers for many kilometers. For everyday riding: a well-geared road bike handles sustained 8–10% fine, and anything that averages over 10% for more than a kilometer deserves respect, a low gear, and a look at your gearing before you go.
How do you find a climb's gradient from a map or Strava?
Three ways, in rising order of usefulness for the whole climb. A road sign in the mountains states the average for the next kilometer — a fair sample, but silent about the ramp around the corner. A map gives you the contour lines or spot heights at the bottom and top for the gain, and the road distance measured along its bends (never the straight line) for the run; divide, and you have the average. A ride file is best: the segment's average grade on Strava or a route planner already did the division over the real road. What you should not use is the live grade field on your bike computer — it describes the last few seconds of road, not the climb. Whatever the source, put gain and distance into the calculator above; a surprising share of forum arguments about a hill's steepness turn out to be two people measuring different distances.
Why does my bike computer's gradient disagree with the sign?
Because they measure different things. The sign is an average over a stretch; the computer estimates the instantaneous slope from its barometric altimeter and your speed, smoothed over a few seconds and lagging slightly behind the road. On a climb that alternates ramps and shelves it will swing from 4% to 14% while the sign says 8%, and both are right. Phones and GPS-only devices are worse — satellite altitude is noisy enough that many of them read the grade off a map instead of measuring it. For pacing, trust the average and your legs; for choosing a gear, trust the maximum, which is the point of the box below.
Two climbs can both "average 6%": one holds a metronomic 6%; the other alternates 12% ramps with flat shelves. The second is meaningfully harder and slower at the same power — the watts you save on the easy stretches never repay the time lost on the steep ones. When a profile shows a spiky climb, read its maximum grade, not its average, to pick your gearing.