Transparency & Science

About &
Methodology

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.

What Is Cycling Calculator?

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 Calculation

The Model

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.

// Base PSI from contact patch theory
PSI = (load_kg × 2.205 × 0.85) / (tyre_width_mm / 25.4)
      × terrain_multiplier
      × rider_comfort_bias
      + profile_pressure_offset

// Weight split: 42% front / 58% rear (road standard)
load_front = total_kg × 0.42
load_rear = total_kg × 0.58

Terrain Multipliers

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:

🛣️
Road (tarmac)
Multiplier: 1.00 — full contact patch pressure, smooth surface, minimal vibration losses
🪨
Gravel / mixed
Multiplier: 0.82 — lower pressure allows casing to absorb surface irregularities, reducing road buzz and improving traction
🏔️
Mountain bike
Multiplier: 0.55 — significantly lower pressure for maximum traction, cornering grip and root/rock absorption

Rider Profile Offsets

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 Calculation

The Core Physics — Why Speed Is Linear, Not Quadratic

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:

// Rolling resistance FORCE (constant — independent of speed)
F_rr = Crr × mass_kg × g
= Crr × (rider + bike) × 9.81 [in Newtons]

// Rolling resistance POWER (linear with speed)
W_rr = F_rr × velocity_ms
W_rr = Crr × mass_kg × g × (speed_kph / 3.6)

// Consequence: doubling speed exactly doubles watts lost to rolling resistance
// 20→40 km/h: watts double. 35→40 km/h: watts increase by 40/35 = 14.3%

// Compare with aerodynamic drag — scales with velocity CUBED:
W_aero = 0.5 × ρ × CdA × v³
// At 40 km/h, aero drag is already 5–10× larger than rolling resistance

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.

Three Independent Variables That Affect Crr

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:

// Full Crr model used in this calculator
Crr = Crr_base × width_factor × pressure_factor

// 1. Surface base Crr (independent of width and pressure)
Crr_base_road = 0.004 // BRR drum-test averages 2020–2023
Crr_base_gravel = 0.008 // Schwalbe / Continental published data
Crr_base_mtb = 0.020 // Academic literature average

// 2. Width factor — wider tyres have lower Crr at optimal pressure
width_factor = (25 / width_mm) ^ 0.10
// Exponent 0.10 fitted to BRR published drum-test data (23–50mm range)
// 23mm vs 45mm at optimal pressure: Crr differs by ~7%

// 3. Pressure factor — asymmetric penalty (this is critical)
optimal_psi = 90 × (25 / width_mm) // Silca contact-patch model
ratio = actual_psi / optimal_psi

// UNDER-inflated (ratio < 1): significant penalty — excess casing flex
if ratio < 1: pressure_factor = 1 + (1 − ratio) × 0.40

// OVER-inflated (ratio > 1): asymmetric — surface-dependent
if ratio > 1 on road: pressure_factor = 1 + (ratio − 1) × 0.05
if ratio > 1 on gravel: pressure_factor = 1 + (ratio − 1) × 0.20
// Over-inflation barely raises Crr on smooth tarmac (tyre already stiff enough)
// But increases it meaningfully on rough surfaces (vibration energy loss)

Why the Pressure Penalty Is Asymmetric

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.

Width Effect: Why Wider Is Not Slower

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.

Base Crr Values by Surface

SurfaceBase CrrSourceConfidence
Smooth tarmac (road)0.004BRR drum-test averages, 2020–2023 (100+ tyres)Good
Gravel / hardpack0.008Schwalbe & Continental published data; Anhalt field testsEstimated
MTB trail / dirt0.020Academic 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 Ratio & Speed Calculation

Gear calculations use exact mechanical relationships — these are mathematically precise, not estimates.

// Gear ratio
ratio = chainring_teeth / sprocket_teeth

// Wheel circumference (using nominal diameter)
circumference_m = (wheel_diameter_mm / 1000) × π

// Speed
speed_kph = ratio × cadence_rpm × circumference_m × 60 / 1000

// Rollout (distance per pedal revolution)
rollout_m = ratio × circumference_m

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 Zones

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.

FTP & Power Zone Calculation

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.

// Zones as percentage of FTP
Z1 Active Recovery : 0–55% of FTP
Z2 Endurance : 56–75% of FTP
Z3 Tempo : 76–90% of FTP
Z4 Threshold : 91–105% of FTP
Z5 VO₂ Max : 106–120% of FTP
Z6 Anaerobic Cap. : 121–150% of FTP
Z7 Neuromuscular : 150%+ of FTP

// FTP estimation from 20-min test
FTP ≈ 20_min_power × 0.95

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.

Tyre Width & Rim Compatibility

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.

Power vs Speed Calculation

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.

// Total power required (watts)
P_total = (F_gravity + F_rolling + F_aero) × velocity / η

// Gravitational force (watts on gradient)
F_gravity = mass_kg × 9.81 × sin(arctan(grade/100))

// Rolling resistance force
F_roll = mass_kg × 9.81 × cos(arctan(grade/100)) × Crr

// Aerodynamic drag force
F_aero = 0.5 × ρ × CdA × (v + v_wind)²

// Constants: ρ = 1.225 kg/m³ (sea level), η = 0.975 (drivetrain efficiency)

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).

Hill Climb & VAM Calculation

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:

// VAM — vertical metres per hour
VAM = elevation_m / (time_min / 60)

// Speed from distance and time
speed_kph = (length_m / 1000) / (time_min / 60)

// Power using full physics model
gradient = (elevation_m / length_m) × 100
P = (F_gravity + F_roll + F_aero) × velocity / 0.975

// W/kg
W_per_kg = P_watts / rider_kg

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.

Aerodynamics (CdA) Calculation

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.

// Isolate aerodynamic force from measured power
F_drive = P_watts × η / velocity
F_roll = mass_kg × 9.81 × Crr
F_aero = F_drive − F_roll

// Solve for CdA
CdA = F_aero / (0.5 × ρ × velocity²)

// Assumes: flat terrain, no wind, ρ = 1.225 kg/m³, η = 0.975

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.

Calories & Nutrition Calculation

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.

// MET-based calorie calculation
kcal = MET × body_mass_kg × duration_hours

// Example MET values (2024 Compendium)
Road cycling 16 km/h → MET ≈ 5.8
Road cycling 24 km/h → MET ≈ 9.6
Road cycling 32 km/h → MET ≈ 11.8
MTB (general) → MET ≈ 8.5–11

// Energy substrate split (moderate intensity)
Carbohydrate ≈ 55% of kcal → grams = (kcal × 0.55) / 4
Fat ≈ 35% of kcal → grams = (kcal × 0.35) / 9

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 (TSS, IF, TSB) Calculation

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.

// Intensity Factor
IF = NP / FTP // where NP = Normalised Power

// Training Stress Score
TSS = (duration_hours × NP × IF / FTP) × 100

// Chronic Training Load (42-day exp. weighted avg)
CTL_today = CTL_yesterday + (TSS_today − CTL_yesterday) / 42

// Acute Training Load (7-day exp. weighted avg)
ATL_today = ATL_yesterday + (TSS_today − ATL_today) / 7

// Training Stress Balance (Form)
TSB = CTL − ATL

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.

Scientific References & Sources

Book
Training and Racing with a Power Meter
Hunter Allen & Andrew Coggan, Ph.D. — VeloPress, 3rd Ed. 2019
Source of 7-zone FTP model, W/kg classifications
Academic Paper
Preferred pedalling cadence in professional cycling
Lucia A, Hoyos J, Chicharro JL — Medicine & Science in Sports & Exercise, 33(8), 2001
Cadence zone data
Industry Research
Silca Tyre Pressure Guide
Josh Poertner, Silca LLC — silca.cc/blogs/friday-tech-roundup
Contact patch theory, pressure-width relationships
Testing Lab
Bicycle Rolling Resistance Database
bicyclerollingresistance.com — Independent drum-test measurements
Crr values for road tyres
Book
The Bicycle Wheel
Jobst Brandt — Avocet, 3rd Ed. 1993
Mechanical principles of wheel and tyre physics
Standard
ETRTO Standards Manual
European Tyre & Rim Technical Organisation — etrto.org
ISO 5775 tyre/rim sizing and compatibility rules
Journal
Bicycle Quarterly
Jan Heine, editor — bikequarterly.com
Real-world tyre testing, pressure and rolling resistance research
Academic Paper
Modelling the power-speed relationship in cycling
Bassett DR, Kyle CR, Passfield L et al. — Int. J. Sports Physiol. Perform., 1999
Climbing power and VAM reference values
Book
High-Performance Cycling
Asker E. Jeukendrup (Ed.) — Human Kinetics, 2002
CdA values by position, power vs speed modelling
Academic Paper
Nutrition for endurance sports
Jeukendrup AE — Sports Medicine, 41(11), 2011
Carbohydrate intake guidelines during prolonged cycling
Reference Database
2024 Compendium of Physical Activities
Ainsworth BE et al. — Medicine & Science in Sports & Exercise
MET values for cycling at all intensities and terrain types
Academic Paper
Modeling elite athletic performance
Banister EW — Physiological Testing of Elite Athletes, 1991
CTL/ATL time constants and TSB form model
Industry White Paper
Virtual Elevation (Chung Method)
Robert Chung — Validation and field-testing methodology, 2012
CdA estimation from field power and speed data

Accuracy & Limitations

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.

CalculatorExpected AccuracyKey Variables Not Modelled
Tyre Pressure±5–10 PSI of optimalTyre casing construction, tubeless vs tubed, temperature, rider position
Rolling Resistance±20–30% on unpavedSurface moisture, tyre compound, tread pattern, temperature
Gear & SpeedExact (pure maths)Drivetrain efficiency losses (~2–4%), tyre deflection at load
Power vs Speed±5% flat/calm conditionsWind direction, altitude, varying gradient, rider mass distribution
Hill Climb / VAM±5–10% steady climbsMid-climb descents, variable pacing, position changes on climb
Aerodynamics (CdA)Indicative estimate onlyWind, gradient, rider position variation, tyre Crr assumption
Power Zones / TSSExact given correct FTPDaily fatigue, altitude, heat stress, fitness changes over time
Calories±15–20% individual variationRider fitness level, temperature, course variability, drafting
Tyre Width / RimPer ETRTO standardBrand-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.

About This Project

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.