A wearable's display dominates its power budget far more than a phone's, because the screen is the only subsystem active nearly 100% of the time. This model separates two operating modes, each with its own duty cycle:
P_display = P_base + n_lit · p_pixel · brightness
Ambient: sparse monochrome digits, 1–60 Hz redraw, dim
Active: full-color face, 60 Hz, bright — n_lit and p_pixel both jump
P_total = P_display + P_complication + P_radio_sync + P_wake
P_complication ∝ (updates/min) · E_cpu_wake (CPU wake to redraw a tile)
P_radio_sync ∝ (syncs/min) · E_ble_packet (BLE connection event, phone↔watch)
P_wake ∝ (raises/min) · E_gesture_wake (accelerometer IRQ → full activation)
battery(t) = battery(0) − ∫ P_total(t) dt / (V · C_mAh)
- Ambient vs Active — AOD keeps most AMOLED pixels off (true blacks cost ~0 power per-pixel) and redraws only the digits/hands at a low rate; Active lights the whole panel at full brightness every frame, which is why raising your wrist for even a few seconds costs disproportionately more energy than an hour of ambient ticking.
- Complications — each watch-face tile (heart rate, weather, steps) that refreshes wakes the CPU briefly even in ambient mode; more tiles/minute directly raises baseline draw.
- Phone sync — WatchConnectivity / Wearable Data Layer transfers happen over a low-energy BLE connection; every additional sync per minute adds one radio connection event's worth of energy.
- Raise-to-wake — each gesture triggers a full-brightness Active burst before the display times back out to ambient, so its per-event cost is set by the Active power level, not the Ambient one.
Real-world relevance: this is exactly the trade-off Apple Watch's watchOS and Wear OS scheduler tune automatically — capping complication budgets and coalescing BLE syncs — to hit their advertised 18–36 hour battery life.