How a timer counts

A timer is a peripheral that counts clock pulses on its own, while the CPU does other work. Three settings decide how it counts: the prescaler, the counter and the auto-reload value.

Clock and timer are not the same

The clock is the oscillator that drives the whole chip. A timer is a peripheral that counts clock ticks and fires events. Timers measure time, make PWM signals on a pin, interrupt the CPU at a fixed rate and measure outside signals.

Timer block diagram: the clock goes through the prescaler into the counter

Three settings

Prescaler (PSC) divides the input clock, so the timer counts slower.
Counter: the register that goes up by one on every timer tick. On TIM1 it is 16 bits wide: 0 to 65535.
Auto-reload register (ARR): the top value. After the counter reaches ARR, the next tick takes it back to 0. That moment is called an update event. In CubeMX, ARR is called Counter Period.

f_timer = f_clock / (PSC + 1)

The +1 is there because PSC = 0 means "divide by 1". f_clock is the clock going into the timer; f_timer is how fast it counts.

Example: a 16 MHz clock and PSC = 15999 give 16 000 000 / 16 000 = 1000 counts per second: one count every millisecond.

Counting modes

Up (the default): 0 up to ARR, then back to 0
Down: ARR down to 0, then back to ARR
Center-aligned: 0 up to ARR, then back down to 0