Duty Cycle Calculator

A pulse wave is a part-time signal, and its duty cycle is the fraction of each period it spends on. Enter the pulse width and the frequency, and this calculator returns the duty percentage — and the average voltage the wave delivers, which is what loads actually feel, from dimmer racks to injector drivers.

On-Time Over Period: The Whole Definition, Honestly

Duty cycle is a ratio wearing a percent sign: pulse width ÷ period × 100, where the period is the frequency’s reciprocal (at 1,000 Hz, exactly 1 ms). Nothing else enters — not the voltage, not the shape of the edges (in the ideal) — which is why the quantity travels across every domain that pulses: electronics, where it throttles motors and dims lamps; mechanics, where fuel injectors and solenoids are rated by it; medicine, where pulsed lasers and ultrasound quote it for safety; even radar, whose duty cycle caps average power against a peak the transmitter brags about. The calculator’s third field adds the consequence loads care about: the average a steady load experiences is the peak times the duty fraction — a 5 V wave at 30% presents, to anything slower than the pulses, as 1.5 V of honest direct current.

Worked Example: 0.3 Milliseconds in a 1-Millisecond World

The defaults run a bench-standard case: a 0.3 ms pulse at 1,000 Hz. The period is 1.000 ms, so the duty cycle is 0.3 ÷ 1.000 = 30.0%, the signal resting for 0.700 ms of every millisecond, and at the default 5 V peak the average is 1.50 V — the figure an LED dimmer or a small motor actually obeys. Slide the pulse to 0.5 ms and the wave becomes the true square wave (50.0%, average 2.50 V), the clock signal’s symmetric ideal; slide it to 0.02 ms and you hold a 2% strobe, all peak and no presence. One ratio, three personalities — and the calculator’s refusal line deserves its fame: a pulse wider than its period is not a big duty cycle but a category error, a signal that never turns off, which the widget names rather than computes.

PWM: The Duty Cycle as a Control Knob

Pulse-width modulation turns this page’s ratio into engineering’s favourite dimmer: hold the frequency fixed, vary the duty, and average power follows linearly — an LED at 30% duty glows at (perceptually, nearly) 30% brightness while its junctions only ever see full current or none, which keeps colour and efficiency honest in a way analogue dimming cannot. Motor drives, switch-mode power supplies, servo positioning (where the width itself is the message — 1 ms versus 2 ms commanding opposite extremes at a stately 50 Hz), and class-D audio all run on the same exchange: timing precision, which digital systems have in abundance, traded for amplitude precision, which they lack. The calculator’s average-voltage line is PWM’s whole theory in one multiplication — and its frequency-independence is the surprise newcomers should sit with: at fixed duty, 100 Hz and 100 kHz deliver the same average; only the ripple’s smoothness negotiates.

The Heartbeat Precedent

Nature computed duty cycles first: a resting heart spends roughly a third of each cycle contracting (systole) and two thirds refilling — a duty cycle near 35% at 60 beats per minute — and exercise physiology is partly the study of diastole’s share shrinking as rate climbs, which is why very high heart rates starve the very filling they depend on. Engineered systems inherit the same bind: a converter or an injector driven toward 100% loses the off-interval its physics needed (inductor reset, injector closing, muscle reperfusion), and maximum-duty specifications are confessions of where the off-time stops being negotiable. The calculator’s cheerful ratio thus carries a universal warning label, legible from cardiology to power electronics: the off-time is not waste; it is where the next cycle is prepared. Designs that forget this — in silicon or in training plans — discover the same physiology: a system pinned at a hundred percent has nowhere to recover in, and its failure arrives not as decline but as collapse.

Mark-Space: The Ratio’s Other Name

Telegraphy named this ratio first — mark for the on, space for the off — and the mark-space ratio governed everything from Morse keying to the baudot machines’ mechanical governors. The lineage matters because it reveals the quantity’s true generality: any system that alternates between two states on a schedule has a duty cycle, and its average behaviour is the duty-weighted average of the states — true for current in a wire, torque from an engine’s power strokes, light from a lighthouse’s rotating shutter (whose duty, by design, is tiny and whose peak is enormous), and attention in a Pomodoro timer. The calculator computes the electrical dialect, but the reader who sees the pattern owns the concept everywhere: when something pulses, ask for the fraction, and the averages will follow — power, brightness, torque, dose and flow are all the same weighted sum wearing different units.

Related Tools

More from the Other Calculators hub: the Op-Amp Gain Calculator for the stages that condition these pulses, and the Streaming Bitrate Calculator — a different kind of rate, the same habit of multiplying honestly.

Frequently Asked Questions

Can duty cycle exceed 100%?

Not for a single pulse train — the on-time cannot exceed the period that contains it, and the calculator refuses the input rather than printing nonsense. Figures above 100% do appear in one legitimate costume: overlapping phases (a three-phase motor drive’s combined conduction, or interleaved converter phases) can sum past 100% across channels, which is a statement about a system, not about any one wave. If a datasheet quotes a device at 120% duty, it is describing such a sum or a marketing dialect; the single-wave definition on this page is the court of appeal, and it caps at 100 with the signal simply on.

How do I measure duty cycle on an oscilloscope?

Read the pulse width at the 50% amplitude points (the standard’s definition — edges are measured mid-swing, not at the baseline where noise fuzzes them), read the period between corresponding edges, and divide: this calculator with your two numbers. Bench scopes compute it automatically from the same landmarks, and the agreement is a good calibration of both. The mid-swing convention matters at slow edges: a lazy rise spends real time between 10% and 90%, and where you call the edge moves the width — the 50% rule exists so that two honest engineers with the same waveform file the same report.

Why does my servo expect 1–2 ms pulses at 50 Hz?

Because the hobby servo standard encodes position in width against a 20 ms frame (50 Hz): 1 ms commands one extreme, 1.5 ms the centre, 2 ms the other — a duty cycle of only 5–10%, with the vast off-time serving as the frame that makes the width legible. It is PWM’s information mode rather than its power mode (the motor inside does its own power PWM at inaudible rates), and this calculator shows the oddity plainly: a control channel running at single-digit duty, where the absolute width, not the percentage, carries the meaning — a reminder that the ratio rules power, while the width itself can be a language.

What frequency should PWM use for LEDs and motors?

Above the flicker and hearing thresholds for comfort — LEDs are commonly driven past 200 Hz (and far higher where cameras film them, since rolling shutters band against slow PWM), motors from a few kHz into the ultrasonic (16–25 kHz) so the drive does not sing. The trade is switching loss: every transition wastes a little energy in the switch, so frequency is spent deliberately. The calculator’s contribution is the independence result in the PWM section: whatever frequency the acoustics choose, the duty-to-average arithmetic is untouched — set the percentage here, set the frequency there, and the two decisions never quarrel.

How does duty cycle relate to a signal’s RMS?

For a rectangular wave switching between 0 and V, the RMS is V × √(duty fraction) — the square root appears because power goes as voltage squared, and RMS is the power-equivalent voltage. At the worked example’s 30%, RMS is 5 × √0.3 ≈ 2.74 V — distinctly more than the 1.50 V average, and the difference matters: heating follows RMS (power), while electrochemistry and meter movements follow the average. Confusing the two is the classic duty-cycle error; this page prints the average (the PWM-control figure), and this answer supplies the RMS for the heating questions, with the square root flagged as the entire distinction.

What is duty cycle in a fuel injector or solenoid?

The same ratio at mechanical scale: an injector commanded for 12 ms of every 20 ms cycle is at 60% duty, delivering roughly 60% of its full-flow fuel (plus opening/closing transients the engineers model separately) — engine controllers literally schedule fuel in duty terms at high load, and an injector pinned at 100% (static, fully open) is the system’s confession that the fuelling demand exceeded the hardware. Solenoids and proportional valves quote maximum duty against heating: the coil’s RMS current is the duty’s child, as the previous answer’s square root predicts. One ratio, from nanoseconds to engine bays — and the mechanic reading a duty figure on a scan tool and the engineer reading one on a scope are, whether they know it or not, colleagues in the same small science.