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Instrument MI-14-070 · Other

Duty Cycle Calculator

Enter how long a pulse stays on and the full period it repeats within, and this instrument returns duty cycle — the percentage of each period a signal spends switched on, the core measure behind PWM.

Instrument MI-14-070
Sheet 1 OF 1
Rev A
Verified
Type 14 — Networking & Data Transfer SER. 2026-14070

Duty cycle (%)

30.0000

duty cycle = (on time / period) x 100%

The working Every figure verified twice
  1. dutyCyclePct = 3 ⁄ 10·100 = 30.0000
Worksheet log
  1. No entries yet — change an input to log a scenario.

How this instrument works

Duty cycle describes what fraction of a repeating signal's period is spent in the 'on' state, expressed as a percentage. A signal that's high for 3 milliseconds out of every 10-millisecond period has a 30% duty cycle: three-tenths of each repeat spent on, seven-tenths spent off. It's a ratio, so it applies identically whether the period is measured in milliseconds, microseconds, or seconds — only the on-time and period need to share the same unit.

Duty cycle is the central parameter in pulse-width modulation (PWM), the technique of encoding an analog-like value — motor speed, LED brightness, average voltage — into a digital on/off signal by varying how much of each period stays high. A reading of 100% is fully on with no switching at all, 0% is fully off, and 50% spends equal time in each state; everything in between delivers a proportionally scaled average power or voltage to whatever the signal drives, without ever using an intermediate voltage level itself.

Because duty cycle only measures the shape of one period, it says nothing on its own about how fast that period repeats — a 30% reading at 100 Hz and a 30% reading at 100 kHz look identical as a percentage, even though the second one is switching a thousand times faster. Frequency (how many times the period repeats per second) and duty cycle (how that single cycle is split between on and off) are independent settings that together fully describe a PWM signal.

D%=tonT×100D\% = \dfrac{t_{on}}{T} \times 100
on time — duration the signal spends high within one cycle · period — the full duration of one repeating cycle, on time plus off time · duty cycle — the percentage of the period spent on, from 0% (always off) to 100% (always on).
  • Enter On time (ms) — how long the signal stays in its 'on' or high state during one cycle.
  • Enter Period (ms) — the full duration of one repeat of the signal, on time plus off time combined.
  • Read Duty cycle (%) directly — this is (on time / period) x 100, the percentage of each cycle spent on.
  • On time cannot exceed the period, since a signal can't be on for longer than one full cycle lasts — the instrument will prompt you if it does.
  • Period must be greater than zero, and on time cannot be negative; the instrument will prompt you if either falls outside that range.

Worked example — 3 ms on within a 10 ms period

Enter On time (ms) = 3 and Period (ms) = 10 — a signal that's high for 3 ms out of every 10 ms period, the kind of pulse you'd see from a 100 Hz PWM signal (since a 10 ms period repeats 100 times per second). Dividing gives 3 / 10 = 0.3, and multiplying by 100 gives 30. Duty cycle reads 30%.

That 30% figure means the signal spends 3 ms on and the remaining 7 ms off in every period, regardless of how fast those periods repeat. If the same 3 ms on-time occurred within a shorter 6 ms period instead, duty cycle would rise to 3 / 6 x 100 = 50%, since the same on-time now fills a larger share of a shorter period.

Questions

What does a 50% duty cycle actually look like?

It's a signal that spends exactly half of each period on and half off — a standard square wave, symmetric between its high and low states. It's the midpoint of the duty cycle scale: below 50% the signal is off more than it's on, and above 50% it's on more than it's off.

Can on time be equal to the period?

Yes — that gives a 100% duty cycle, meaning the signal is on for the entire period with effectively no off time at all, equivalent to a constant 'on' signal rather than a pulsing one. On time can equal but never exceed the period, since a pulse can't stay on for longer than one full period lasts.

How is duty cycle related to a signal's frequency?

They're independent parameters that describe different things. Frequency is how many times the period repeats per second (its reciprocal), while duty cycle is what fraction of each individual cycle is spent on. Two signals can share the same duty cycle at wildly different frequencies — a 30% reading looks identical as a percentage whether the underlying period repeats 100 times a second or 100,000 times a second.

Why is duty cycle central to pulse-width modulation (PWM)?

Because PWM encodes an analog-like value — LED brightness, motor speed, average output voltage — purely by varying how much of each period stays on, without ever generating an intermediate voltage itself. Raising the duty cycle raises the average power delivered over time; a dimmer LED and a brighter LED driven by the same PWM circuit differ only in duty cycle, not in the peak voltage applied.

Why can't duty cycle be calculated if the period is zero?

Because dividing on time by a zero-length period is mathematically undefined — a period of zero would mean it has no duration to divide into on and off portions at all. Period must be a positive number greater than zero for a duty cycle percentage to have any meaning.

References