Fitness-Fatigue Model Calculator
The Banister fitness-fatigue model treats performance as the balance of two decaying traces driven by training load: fitness builds slowly and fades slowly, while fatigue rises sharply and clears quickly. Predicted performance is a baseline plus a gain times the fitness trace, minus a larger gain times the fatigue trace. This calculator advances the model by one day. You enter yesterday's fitness and fatigue values, today's training load, the two time constants, the two gains, and a baseline, and it returns today's updated fitness, fatigue, and predicted performance. The time constants and gains must be fitted to the individual, so they are all user-editable inputs rather than fixed assumptions.
Banister one-day update
new fitness = old fitness * e^(-1 / tau1) + today load
new fatigue = old fatigue * e^(-1 / tau2) + today load
predicted performance = baseline + k1 * new fitness - k2 * new fatigue
form = k1 * new fitness - k2 * new fatigue
Worked example: old fitness 100, old fatigue 60, today load 50, tau1 42, tau2 7. New fitness = 100*e^(-1/42) + 50 = 147.65. New fatigue = 60*e^(-1/7) + 50 = 102.00. With k1 = 1, k2 = 2, baseline 0, performance = 147.65 - 204.01 = -56.36.
Model notes
- Fitness decays slowly and fatigue decays fast, set by the two time constants.
- Time constants and gains must be fitted per athlete; they are editable inputs here.
- Enter zero load on a rest day to watch both traces decay.
- Reducing load before competition lets fatigue fall while fitness lingers.
- Use a consistent load unit matching the units the gains were fitted in.
Fitness-fatigue model: frequently asked questions
What is the Banister fitness-fatigue model?
The Banister impulse-response model represents performance as the difference between two traces built from training load: a slow-decaying fitness trace and a fast-decaying fatigue trace. Predicted performance equals a baseline plus a fitness gain factor times the fitness trace minus a fatigue gain factor times the fatigue trace.
How does this calculator step the model forward?
It advances one day. New fitness equals yesterday's fitness times e to the power of minus 1 over the fitness time constant, plus today's training load. New fatigue uses the same form with the shorter fatigue time constant. Predicted performance is then baseline plus k1 times fitness minus k2 times fatigue.
What are typical time constants?
Classic studies often use a fitness time constant around 42 days and a fatigue time constant around 7 days, with the fatigue gain larger than the fitness gain. These values vary by athlete and study and are user-editable here, because they must be fitted to an individual rather than assumed.
What is training load in this model?
Training load is any consistent daily load measure, commonly a TRIMP score. The model is unit-agnostic: enter today's load in the same units used to fit the gains and time constants. Enter zero on a rest day to see fitness and fatigue decay.
Why does fatigue decay faster than fitness?
The model uses a shorter time constant for fatigue so that the negative fatigue trace fades quickly after training while the positive fitness trace lingers. This produces the familiar pattern where reducing load before competition lets fatigue drop while fitness remains, improving predicted performance.
Official sources
- National Center for Biotechnology Information (PubMed): Banister impulse-response model literature.
- American College of Sports Medicine: Training load and performance modelling resources.
Reviewed by the CalculatorHub team, edited by James Graham, 17 June 2026. See our methodology.