Every calculation on this site is grounded in established cycling physics and published research. This page explains how each of the 10 tools works, what assumptions are made, and where the science comes from.
Cycling Calculator is a free, browser-based performance tool for road, gravel, and mountain bike riders. It covers five key areas of cycling performance: tyre pressure optimisation, rolling resistance estimation, tyre width selection, gear ratio and speed calculation, and FTP-based power zone analysis.
The tool is designed to help riders of all levels — from beginners finding their first PSI setting to competitive racers dialling in marginal gains — make more informed decisions about their equipment setup. All calculations run locally in your browser. No data is sent to a server.
Tyre pressure recommendations are derived from a contact patch load model, originally developed by Silca (Josh Poertner) and validated against data published by Jan Heine at Bicycle Quarterly. The fundamental principle is that an optimal tyre contact patch shape (slightly wider than tall) minimises both rolling resistance and energy loss from casing flex.
Different surfaces require different pressure adjustments. Our multipliers are based on data from Silca's published tyre pressure guides and SRAM's AXS tyre pressure calculator:
Profile adjustments reflect rider priorities rather than physics. A racing rider accepts lower comfort for marginally better rolling efficiency; a bikepacking rider prioritises flat prevention over rolling speed. These offsets are informed by real-world recommendations from coaches and professional mechanics.
"The ideal tyre pressure is the lowest pressure that prevents pinch flats and rim strikes at your weight, on your terrain. Everything above that is comfort versus speed trade-off." — Josh Poertner, Silca
Rolling resistance is fundamentally different from aerodynamic drag. The rolling resistance force (Frr) is constant — it does not change with speed. Power is force multiplied by velocity, so rolling resistance watts scale linearly with speed:
This linearity is an important and often misunderstood property. Going from 35 to 40 km/h adds the same absolute watts from rolling resistance as going from 10 to 15 km/h. In contrast, aerodynamic drag adds exponentially more watts at higher speeds. This is why at race speeds (>35 km/h), investing in aerodynamics returns vastly more than tyre selection.
Our model correctly treats tyre width, tyre pressure, and surface type as three independent influences on Crr — not a single combined factor. The full adjusted Crr formula is:
This asymmetry is one of the most important and least-documented aspects of tyre physics. Under-inflation forces the casing to deform excessively on each rotation, dissipating energy as heat in the rubber — a large, progressive penalty. Over-inflation on smooth tarmac produces a slightly smaller contact patch but the casing is still deforming efficiently; the penalty is small. However, on rough surfaces (gravel, MTB), an over-inflated tyre cannot conform to surface irregularities, so the rider's body absorbs vibration energy instead — this is sometimes called "impedance loss" and is why higher pressure does not always equal lower rolling resistance in real-world conditions.
This explains the well-documented finding by Jan Heine (Bicycle Quarterly) that the fastest tyre is not always the hardest tyre — particularly on anything other than billiard-smooth tarmac.
The width factor (25/width)^0.10 is an empirical fit to published drum-test data from Bicycle Rolling Resistance across 23–50mm tyres of comparable construction quality, measured at each tyre's own optimal pressure. The effect is real but modest: a 45mm tyre at optimal pressure has approximately 7% lower Crr than a 23mm tyre at its optimal pressure. Over a 100 km road ride at 30 km/h, this translates to roughly 3–5 fewer watts — meaningful but not transformative on its own.
| Surface | Base Crr | Source | Confidence |
|---|---|---|---|
| Smooth tarmac (road) | 0.004 | BRR drum-test averages, 2020–2023 (100+ tyres) | Good |
| Gravel / hardpack | 0.008 | Schwalbe & Continental published data; Anhalt field tests | Estimated |
| MTB trail / dirt | 0.020 | Academic literature average (Brandt, Wilson) | Estimated |
Crr on unpaved surfaces varies enormously with moisture, soil type, and tread pattern. The gravel and MTB values are conservative mid-estimates. Real-world conditions may produce values 30–50% higher or lower. Always treat unpaved Crr as approximate.
Gear calculations use exact mechanical relationships — these are mathematically precise, not estimates.
Wheel diameter values follow ISO 5775 / ETRTO standards for tyre and rim sizing. The 700c (622mm bead seat diameter) value used is the internationally standardised measurement, not the nominal outer diameter.
Cadence zone boundaries are based on guidelines from USA Cycling coaching materials and the findings of Lucia et al. (2001), which established that professional cyclists self-select cadences of 80–100 RPM during sustained efforts. Higher cadences (100–120 RPM) are associated with reduced muscular fatigue at equivalent power outputs.
Power zones are calculated using the 7-zone model developed by Andrew Coggan, Ph.D., as published in Training and Racing with a Power Meter (Allen & Coggan, 2010) and subsequently adopted by TrainingPeaks, Garmin, and most major cycling training platforms.
The W/kg (watts per kilogram) classification thresholds used in our tool are derived from Coggan's cycling power profile charts and reflect typical performance ranges for male riders at sea level. Female rider thresholds are typically 10–15% lower due to physiological differences in muscle mass ratio.
Rim-to-tyre compatibility calculations follow ETRTO (European Tyre and Rim Technical Organisation) standards, specifically the guidelines published in the ETRTO Standards Manual. The recommended tyre width range for a given internal rim width is 1.45× to 2.05× the internal rim width.
This rule ensures proper tyre seating, prevents dangerous blow-offs, and maintains the designed tyre profile. Deviating significantly from this range can result in unpredictable handling, reduced puncture protection, and in extreme cases, tyre failure.
The Power vs Speed calculator uses a full physics resistance model that accounts for every meaningful force acting on a cyclist. It can solve in both directions: given speed, calculate required watts; or given watts, calculate expected speed.
CdA values for each riding position are based on published data from Jeukendrup & Martin (2001) and validated against wind tunnel measurements published by Specialized and Cervélo. The 97.5% drivetrain efficiency figure is the midpoint of the 95–99% range measured by Friction Facts (now Ceramic Speed).
VAM (Velocità Ascensionale Media) was developed by Dr. Michele Ferrari and popularised through its use in professional cycling analysis. The relationship between VAM and W/kg at a given gradient is well-established:
The climb calculator uses a climbing-specific aerodynamic coefficient (CdA = 0.38 m²) appropriate for an upright road position at low speeds, and a slightly elevated Crr (0.006) for road tarmac under load. These values match those used in the academic analysis published by Bassett et al. (1999) in the International Journal of Sports Physiology and Performance.
The CdA estimator uses a simplified inverse power model: given measured power and speed on flat terrain, it back-calculates the aerodynamic drag area after subtracting rolling resistance and drivetrain losses.
This is a simplified version of the Chung Method (Robert Chung, 2012), which uses repeated laps of a loop and regression analysis to simultaneously solve for both CdA and Crr. Our single-effort estimate is useful for position comparison but carries greater uncertainty than a full Chung analysis. For reference CdA values by position, we cite Jeukendrup (2002), High-Performance Cycling and wind tunnel data published by Swiss Side and Drag2Zero.
Calorie expenditure is estimated using the MET (Metabolic Equivalent of Task) method, with values sourced from the 2024 Compendium of Physical Activities (Ainsworth et al.) — the most comprehensive and widely-cited reference for exercise energy expenditure in sport science.
The carbohydrate/fat energy split is derived from the classical work of Brooks & Mercier (1994) on the crossover concept in exercise metabolism, adapted for moderate-intensity cycling. Fuelling recommendations (gel counts, water volume, timing) follow guidelines from Jeukendrup (2011) published in Sports Medicine: "Nutrition for endurance sports: marathon, triathlon, and road cycling."
Training load metrics use the methodology developed by Andrew Coggan, Ph.D. and described in detail in Training and Racing with a Power Meter (Allen & Coggan). These metrics are the foundation of virtually all power-based training platforms.
The time constants of 42 days (CTL) and 7 days (ATL) are empirically derived and represent the approximate timeframes over which fitness accumulates and fatigue dissipates respectively. These constants were established through analysis of professional cyclist training data and validated in peer-reviewed literature including Banister et al. (1991), "Modeling elite athletic performance," in Physiological Testing of Elite Athletes.
This tool provides estimates and starting points, not precision engineering results. Use these results as an informed starting point, then fine-tune based on your personal feel and experience.
| Calculator | Expected Accuracy | Key Variables Not Modelled |
|---|---|---|
| Tyre Pressure | ±5–10 PSI of optimal | Tyre casing construction, tubeless vs tubed, temperature, rider position |
| Rolling Resistance | ±20–30% on unpaved | Surface moisture, tyre compound, tread pattern, temperature |
| Gear & Speed | Exact (pure maths) | Drivetrain efficiency losses (~2–4%), tyre deflection at load |
| Power vs Speed | ±5% flat/calm conditions | Wind direction, altitude, varying gradient, rider mass distribution |
| Hill Climb / VAM | ±5–10% steady climbs | Mid-climb descents, variable pacing, position changes on climb |
| Aerodynamics (CdA) | Indicative estimate only | Wind, gradient, rider position variation, tyre Crr assumption |
| Power Zones / TSS | Exact given correct FTP | Daily fatigue, altitude, heat stress, fitness changes over time |
| Calories | ±15–20% individual variation | Rider fitness level, temperature, course variability, drafting |
| Tyre Width / Rim | Per ETRTO standard | Brand-specific tolerances, hookless rim restrictions |
Always verify tyre pressure with a calibrated floor pump gauge before riding. Digital gauges are significantly more accurate than analogue gauges at the low pressures used in gravel and MTB riding.
cycling-calculator.com is an independent, ad-supported free tool built by a cycling enthusiast. It covers 10 calculators across tyres, gears, climbing, aerodynamics, and training. It has no affiliation with any tyre brand, component manufacturer, or training platform. Tool recommendations are not paid endorsements.
The site is maintained as a personal project with the goal of making cycling performance science accessible to every rider, not just those who can afford a coach or sports scientist.
Found an error in our methodology, or want to suggest an improvement? Please get in touch.