Normalized Power (NP)

NP is a weighted average power that reflects the physiological cost of variable efforts better than simple average power. A surgy criterium and a steady tempo ride can have the same average power but very different NPs — the crit's NP will be higher because short hard efforts cost more than easy pedaling saves.

1. Compute rolling 30-second average power at every second.
2. Raise each value to the 4th power.
3. Average those.
4. Take the 4th root. That is NP.

The 30-second rolling window approximates the body's physiological response time — VO2, heart rate, and ventilation respond to changes in effort with time constants on the order of 30 seconds, so the rolling average tracks the body's lagged response rather than instantaneous power. Raising to the 4th power captures the non-linear cost of harder efforts.

NP is the 'fatigue-weighted' power. For an evenly paced ride, NP ≈ average power. A moderately variable road ride runs roughly 5–15% higher, and genuinely surgy efforts like criteriums or mountain-bike races routinely run 15% or more above average. The variability index (VI = NP / AP) quantifies how surgy the ride was.