Climb time calculator

How the climb time calculator works

The calculator takes a climb, your weight and your power, and works out how long the climb will take you and how to pace it. There are three ways to give it a climb: pick one of 101 famous climbs, draw one section by section, or upload a GPX of a route or a ride. All three are handled the same way. The climb is cut into 100-metre pieces, each with its own gradient and altitude, and your time is the sum of the time you spend on each piece.

The physics

On every piece, the calculator finds the steady speed at which the power reaching your back wheel balances the three forces holding you back: gravity, rolling resistance and the air. This is the standard road-cycling power model published by Martin and colleagues in 1998. In their field tests it predicted measured power with an R² of 0.97 and a standard error of 2.7 W. It is the same model we used in our widely shared comparison of Tadej Pogačar’s and Marco Pantani’s ascents of Alpe d’Huez, to see who would be faster on modern equipment.

P·η = v·( m·g·sin θ + Crr·m·g·cos θ + ½·ρ·CdA·(v + w)² )

• P is your power at the pedals and η the drivetrain efficiency: 97.5%, in line with Friction Facts’ tests of a clean, lubricated chain (97.6%).
• m is you plus the bike and kit, g is 9.80665 m/s² and θ is the angle of the road (the arctangent of the gradient).
• Crr is rolling resistance: your tyres’ figure from a steel test drum, on the same scale as bicyclerollingresistance.com (0.0030 for a fast race tyre by default), multiplied by a factor for the road surface (1.2 for good tarmac).
• CdA is your drag area, set by your position: 0.32 m² on the hoods by default, from 0.28 m² with your forearms flat to 0.40 m² sitting upright.
• ρ is air density, worked out for every piece from the standard-atmosphere pressure at its altitude and the temperature you give: 1.20 kg/m³ at sea level at 20 °C, 0.95 kg/m³ at 2,000 m.
• w is the headwind (a tailwind is negative), added to your speed through the air.
• Drafting scales CdA by the share of the air you still push: 75% on a wheel, after Blocken and colleagues (2013), who found the second rider of a pair saves 23–27% close up; 35% in the bunch, well above the 5–10% they measured mid-pack in a 121-rider peloton at racing speed (Blocken et al. 2018), because a group strings out on a climb.
• The equation is solved for v with Newton’s method, and the time for each piece is its length divided by that speed.
• With altitude switched on, your power is reduced by the drop measured in unacclimatised athletes by Bassett and colleagues (1999): about 12% at 2,000 m and 18% at 2,700 m.
• In FTP mode, the power you can hold comes from a rule-of-thumb power–duration curve, P = FTP × (t ÷ 60 min)^−0.05, matched to the climb’s own duration: 105.6% of FTP for 20 minutes, 96.6% for two hours.

What slows you down on a climb

Gravity does almost all of it. For a 70 kg rider on a 9 kg bike at 245 W (3.5 W/kg), this is how the resistance splits by gradient:

That is why watts per kilogram decides climbing speed, and why position, aero kit and drafting make little difference above about 6%. On the gentler stretches the air still matters, which is why the calculator models it on every piece rather than once for the whole climb. Sitting on a wheel at 3.5 W/kg saves 31 seconds up Alpe d’Huez, but 2 minutes 51 seconds on the long, shallow Galibier from Briançon.

What the numbers mean

• Time is the time riding the pacing plan. The time at steady power is shown next to it.
• W/kg is your power divided by your body weight. The physics uses your total weight, bike included.
• Average speed is the climb’s length divided by your time.
• VAM (velocità ascensionale media) is the height you gain per hour: the climb’s height gain divided by your time in hours. It compares climbs of different lengths and gradients better than speed does: 3.5 W/kg up Alpe d’Huez is a VAM of about 1,025 m/h.

Climbing times for famous climbs

Times in hours and minutes, from the calculator, for a 70 kg rider on a 9 kg bike, on the hoods with race tyres, at 20 °C, riding the pacing plan.

How accurate is it?

At the power you enter, in still air, expect to be within a few per cent. Power meters disagree by 1–2%, so the same number on two meters is not quite the same effort. It also ignores the time lost speeding up and slowing down, which on a climb is seconds, not minutes.

How the pacing plan works

The plan cuts the climb into six to ten sections of similar gradient and gives each one a power to hold.

• Sections. The cuts are found by dynamic programming: of every way to split the climb, the one that keeps the gradient within each section as even as possible. No section is shorter than 5% of the climb (or 300 m), so a single steep corner doesn’t get a row of its own, and none is longer than a quarter of it, so a long, steady climb still gets checkpoints.
• Powers. Each section’s power is the fastest way to spend the same effort as riding at your steady power. Effort is measured as normalised power, so the plan never costs more than your steady number. It pushes a little harder on the steep sections, where extra power turns almost entirely into speed, and eases where the road flattens and more of it is lost to the air. No section asks for more than 115% of your power or less than 80%.
• What it saves. On a steady climb, seconds: 1 second on Alpe d’Huez at 3.5 W/kg. On a climb with flat stretches and dips, more: 32 seconds on the Col du Glandon from Rochetaillée at 3 W/kg.

Frequently asked questions

Sources

• Martin JC, Milliken DL, Cobb JE, McFadden KL, Coggan AR. Validation of a mathematical model for road cycling power. Journal of Applied Biomechanics 14(3):276–291, 1998. doi:10.1123/jab.14.3.276
• Bassett DR, Kyle CR, Passfield L, Broker JP, Burke ER. Comparing cycling world hour records, 1967–1996: modeling with empirical data. Medicine & Science in Sports & Exercise 31(11):1665–1676, 1999. doi:10.1097/00005768-199911000-00025
• Friction Facts drivetrain efficiency tests, as reported by CyclingAbout: How much does a dirty chain slow you down?
• Tyre rolling resistance on a steel drum: bicyclerollingresistance.com
• Air pressure with altitude: the International Standard Atmosphere
• Blocken B, Defraeye T, Koninckx E, Carmeliet J, Hespel P. CFD simulations of the aerodynamic drag of two drafting cyclists. Computers & Fluids 71:435–445, 2013. Research portal
• Blocken B, van Druenen T, Toparlar Y, et al. Aerodynamic drag in cycling pelotons: new insights by CFD simulation and wind tunnel testing. Journal of Wind Engineering and Industrial Aerodynamics, 2018. Research portal