Cycling Power Calculator

Cycling power calculation: Total Power = Power against rolling resistance + Power against gravity + Power against air + Drivetrain losses Components (in watts): 1. Rolling resistance: P_rolling = Crr × m × g × v Where: Crr = coefficient of rolling resistance (typically 0.003-0.006 for road tires) m = total mass (kg) g = 9.81 m/s² v = velocity (m/s) 2. Gravitational power (climbing): P_gravity = m × g × sin(arctan(gradient/100)) × v For small angles: P_gravity ≈ m × g × (gradient/100) × v Negative on descents (gravity helps) 3. Aerodynamic drag: P_aero = 0.5 × ρ × CdA × v³ Where: ρ = air density (~1.225 kg/m³ at sea level) CdA = drag area (varies with position) v = velocity (m/s) — cubed dependence! 4. Drivetrain losses: Typically 2-3% of total power P_drivetrain = (P_other) × 0.02-0.03 CdA values (drag area, m²) by position: Upright (city bike, cruiser): 0.50-0.65 Hoods (standard road bike): 0.32-0.40 Drops (aggressive road position): 0.27-0.32 TT position (time trial bars): 0.21-0.27 The cubic relationship makes speed expensive — doubling speed quadruples aerodynamic power. This is why aerodynamics matters more at high speeds. Example: 185 lb rider + bike (84 kg) at 18 mph (8.05 m/s) on flat ground in hoods position. Rolling resistance: 0.005 × 84 × 9.81 × 8.05 = 33 W Gravity: 0 (flat) Aerodynamics: 0.5 × 1.225 × 0.36 × 8.05³ = 115 W Drivetrain: ~5 W Total: ~153 W Same rider on 5% climb at 8 mph (3.58 m/s): Rolling resistance: 0.005 × 84 × 9.81 × 3.58 = 15 W Gravity: 84 × 9.81 × 0.05 × 3.58 = 147 W Aerodynamics: 0.5 × 1.225 × 0.36 × 3.58³ = 10 W Drivetrain: ~6 W Total: ~178 W Notice: aerodynamics negligible on slow climbs; gravity dominates. Same rider on flat at 30 mph (13.4 m/s) in aero position: Rolling resistance: 55 W Aerodynamics (CdA 0.24): 0.5 × 1.225 × 0.24 × 13.4³ = 354 W Drivetrain: ~12 W Total: ~421 W Cubic aerodynamic relationship makes high speeds exponentially expensive. Power output benchmarks: Recreational rider, casual: 100-150W sustainable Recreational rider, fit: 150-200W sustainable Amateur enthusiast: 200-250W threshold Strong amateur: 250-300W threshold Cat 3 racer: 280-330W threshold Cat 1/2 racer: 330-380W threshold Pro continental: 380-430W threshold WorldTour pro: 410-470W threshold Threshold = FTP (Functional Threshold Power) ≈ 1-hour max sustainable power. W/kg (watts per kilogram) for climbing: Recreational: 1.5-2.5 W/kg threshold Amateur fit: 2.5-3.5 W/kg Strong amateur: 3.5-4.5 W/kg Cat 3: 4.0-4.5 W/kg Cat 1: 4.5-5.5 W/kg Pro: 5.5-6.0 W/kg WorldTour Grand Tour climber: 6.0+ W/kg sustained for 30+ minutes Coggan power zones (based on FTP): Zone 1 (recovery): <55% FTP Zone 2 (endurance): 56-75% FTP Zone 3 (tempo): 76-90% FTP Zone 4 (lactate threshold): 91-105% FTP Zone 5 (VO2 max): 106-120% FTP Zone 6 (anaerobic capacity): 121-150% FTP Zone 7 (neuromuscular power): >150% FTP Training typically structured by time in zones. Different physiological adaptations at different zones. Performance metrics: FTP (Functional Threshold Power): max 1-hour sustainable power NP (Normalized Power): variable-effort weighted average IF (Intensity Factor): NP / FTP TSS (Training Stress Score): combined intensity × duration metric W' (W-prime): "matches" — anaerobic capacity These metrics guide training programs and race strategy. Power meters: Pedal-based (Garmin Vector, Favero Assioma): $500-$1,500 Crank-based (Stages, Quarq, 4iiii): $300-$1,500 Pedal+crank: ~$1,000+ Wheel-based: $500-$1,200 Direct drive trainers (with built-in power): $500-$1,500 Most riders verify accuracy through laboratory tests; brand-to-brand variations 2-5% typical. For training: any decent power meter works. For competition: ensure consistent measurement source. Wind considerations: Headwind acts as added drag. Tailwind reduces drag. 10 mph headwind into 20 mph ride = effectively 30 mph air speed → much higher power required. Real-world rides include wind, terrain, equipment, all affecting power-to-speed relationship.