Cardio Training Simulation: Heart-Rate Response Model

Exercise Intensity

Effort 40%

Fitness Level

Workout Profile

Live Vitals

Zone 2 — Fat Burn

Heart rate

70 bpm

Target HR

70 bpm

Calories burned

0.0 kcal

Session time

0:00

How it works

Target heart rate for a given effort is set by the Karvonen formula, using heart-rate reserve (HRR) rather than a flat percentage of HRmax:

HRmax = 220 − age
HRR   = HRmax − HRrest
HR_target = HRrest + intensity × HRR

Real heart rate does not jump to the target instantly — the sinoatrial node and autonomic nervous system drive it there with a lag, modeled here as a first-order relaxation:

dHR/dt = (HR_target − HR) / τ
HR(t+dt) = HR + (HR_target − HR) × (1 − e^(−dt/τ))

τ (the response time constant) is shorter on the way up and longer on the way down (recovery), and both are faster in a trained heart — this is exactly why fitter athletes both spike to their target HR quicker and recover afterward faster. Training zones are bands of %HRmax: Z1 50–60% (warm-up), Z2 60–70% (fat burn), Z3 70–80% (aerobic), Z4 80–90% (threshold), Z5 90–100% (anaerobic/VO2max). Calorie burn uses a heart-rate-based estimate (a Keytel-type regression) that scales with HR, body mass and age each second of the session.

Effort slider — the target intensity as %HRR; in Intervals mode it sets the work-interval effort while rest holds at 30%.
Fitness level — changes resting HR, HRmax, and both response time constants τ.
Workout profile — Steady holds one target; Intervals alternates 2 min at the slider's effort with 1 min of active recovery at 30%.

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