Our climb calculator uses professional-grade cycling physics (the same mathematical models used by WorldTour teams) to predict your time on 90 of the world's most iconic climbs.
Henry Goff
Guest post · Founder of HG.Studio · Website creator for Ian Bibby Coaching · Keen cyclist
When Ian asked me to build his coaching website, I knew we needed something more than just a pretty homepage. Ian's coaching is grounded in data: power numbers, pacing strategies, race-specific preparation. So I wanted to build a tool that reflected that philosophy.
The result is the Climb Calculator, and under the bonnet, it runs on what I believe is one of the most accurate cycling physics models available online. Here's how it works.
01 / The Core Equation
Every pedal stroke fights three forces: aerodynamic drag, gravity, and rolling resistance. Our engine solves the full steady-state power equation rather than working backwards from a rule of thumb:
That might look intimidating, but in plain English: the power you put into the pedals (adjusted for drivetrain efficiency) must equal the combined resistance from wind, gradient, and tyre friction. Change your weight by 2kg, or climb at altitude instead of sea level, and the predicted speed shifts.
Where it does simplify, it says so. The model rides a climb at its average gradient in still air, with a fixed riding position (CdA 0.40 m²) and tyre rolling resistance set for good tarmac. Those are the right assumptions for the overwhelming majority of paved climbs, and the wrong ones for a gravel pass, a cobbled berg, or a day with a headwind.
CdA · ½ρ · v³ + (mg sin θ + Crr · mg cos θ) · v = P · η
02 / Numerical Solver
Speed can't be isolated algebraically from a cubic equation, so we solve it numerically. Resistance rises strictly with speed, which means the equation has exactly one answer — we bracket it and halve the interval until it is pinned to
1e-9
of a metre per second.
It might seem like overkill for a cycling calculator, but precision matters. On a 45-minute climb, a small error in the speed calculation compounds with every metre of elevation gained. Getting it right from the start means your predicted time is genuinely useful, not just a rough estimate.
Slower per step than a tangent-following method, and immune to the corner cases that make one diverge.
03 / Altitude-Aware Air Density
Most calculators assume sea-level conditions. Ours uses the barometric formula to compute real air density at any elevation:
ρ = 1.225 × (1 − 0.0000225577·h)^4.25588
At 2,000m on the Galibier, aerodynamic drag drops by 17.8%. That means you go faster for the same power, but the gradient is usually steeper up there, so the net effect is complex. This is exactly why a proper model matters.
That exponent is 4.25588, not the 5.25588 of the pressure formula: air gets colder as well as thinner, and colder air is denser.
Why does this matter?
It matters least where you would expect it to matter most. On Alpe d'Huez you are climbing at 12 km/h, drag is under 2% of what you are fighting, and ignoring altitude costs about 22 seconds. Where it bites is the long, shallow, high climbs you ride fast: assume sea level on Wuling Pass in Taiwan or Mount Evans in Colorado and you are out by more than six minutes.
04 / Fatigue-Aware Power Model
This is the feature I'm most proud of. Most calculators assume you can hold your FTP forever. Anyone who's ridden a long climb knows that's fantasy. You don't produce the same power at minute 90 as you do at minute 5.
In reality, sustainable power decays with duration — and rises sharply for efforts short enough to dip into your anaerobic reserves. It's a fundamental physiological reality. Our piecewise fatigue model captures both ends:
The number this curve pivots around is your FTP, and FTP has a specific meaning: the power you can hold for roughly 40 to 60 minutes, or about 95% of what you can average for 20 minutes. So the curve passes through 100% at 47 minutes. Anything shorter, you go above it; anything longer, below.
A near-two-hour climb like Mont Ventoux uses vastly different power than a 16-minute Hardknott Pass effort. Our model adjusts automatically. The one caveat: how far above FTP you can go for a few minutes varies a lot between riders, so treat predictions for very short climbs as indicative.
05 / The Key Innovation
Here's the problem most calculators don't solve: power determines speed, speed determines duration, and duration determines how much power you can sustain. These are coupled variables, and you can't calculate one without the others.
Power
FTP × fatigue
Speed
Bracketed bisection
Duration
distance ÷ speed
Fatigue
power decay
The solver iterates until power, speed, and duration reach equilibrium, typically in 3-5 cycles.
This iterative approach means the calculator naturally handles the reality that longer climbs require lower power, which means slower speed, which means even longer duration, which means even more fatigue. It all balances out to a genuine prediction, not the impossibly optimistic times you get from calculators that assume you can hold FTP for two hours straight.
06 / 452 Real-World Iconic Climbs
We didn't just build a calculator and call it done. We loaded it with 452 of the world's most iconic climbs, with verified gradient and distance data from 20 regions.
Whether you're dreaming about Alpe d'Huez, planning for the Stelvio, or training for Hardknott Pass in the Lake District, the data is already there. Just plug in your numbers and see what time the physics predicts.
Alpe d'Huez, Ventoux, Tourmalet, Galibier
Hardknott, Winnats, Bealach na Bà
Stelvio, Mortirolo, Zoncolan, Tre Cime
Angliru, Sa Calobra, Lagos de Covadonga
Mt. Washington, Mt. Lemmon
Mur de Huy, Koppenberg
Furka, Grimsel
07 / Performance Classification
Every result includes your W/kg performance tier, giving you instant context for where you stand:
Beginner
<2.0
Recreational
2.0+
Sportive
2.8+
Club
3.4+
Cat 3/4
3.8+
Cat 1/2
4.2+
Elite
4.8+
Pro
5.5+
W/kg = Watts per kilogram of body weight. The single most important metric in climbing performance.
08 / How We Compare
I researched every major cycling climb calculator available online, from the venerable Kreuzotter (dating back to the early 2000s) to modern platforms like Best Bike Split used by WorldTour teams. The question was simple: does anyone else combine all the features we built?
The honest answer: no. Here's how the landscape looks:
| Feature | Ian Bibby | Broleur | Kreuzotter | BestBikeSplit | Vekta |
|---|---|---|---|---|---|
| Full physics equation | ✓ | ✓ | ✓ | ✓ | ✓ |
| Altitude-aware air density | ✓ | ✗ | ✓ | ✓ | ✓ |
| Fatigue / power decay | ✓ | ✗ | ✗ | ~ | ✓ |
| Iterative coupled solver | ✓ | ✗ | ✗ | ✓ | ? |
| 50+ pre-loaded climbs | ✓ 90 | ✗ | ✗ | ✗ | ? |
| W/kg performance tiers | ✓ | ✗ | ✗ | ✗ | ✗ |
| Free to use | ✓ | ✓ | ✓ | ✗ | ✗ |
The bottom line
Kreuzotter has excellent physics documentation. Best Bike Split is used by WorldTour teams. Vekta has the most sophisticated fatigue model (CP/W'). But none of them offer all six features together in a free, accessible tool with 90 pre-loaded climbs. That's the gap we built this calculator to fill.
The calculator isn't just a toy. It's a genuine coaching tool. Ian uses it with his athletes to:
As a cyclist myself, building this tool was a labour of love. I've spent enough time staring at Strava segments wondering "could I go faster?" to know that most online calculators feel vague and unreliable. I wanted to build something that a data-driven rider could actually trust.
The combination of the full power balance equation, altitude-aware air density, fatigue modelling, and the iterative coupled solver means this is about as accurate as you can get without strapping a power meter to the bike and riding the actual climb.
If you're interested in the technical details, the full physics model documentation is available as a PDF download. And if you want to get faster on climbs for real, talk to Ian.
Written by Henry Goff
Founder of HG.Studio, the creative studio behind ianbibby.cc. Keen cyclist and builder of data-driven tools.