RL filter cutoff calculator

The cutoff frequency of a first-order RL filter is the corner where the magnitude response is three decibels down from the passband, set by the ratio of resistance to inductance. In SI units the formula is simple and universal for both the low-pass and high-pass single-pole RL sections: fc equals R divided by two pi L, with R in ohms, L in henries, and fc in hertz. The same numbers also give the angular cutoff omega-c equals R over L in radians per second and the RL time constant tau equals L over R in seconds, so one request can feed Bode estimates, settling windows, and lab notebook checks at once. Students size series inductors and resistors for audio crossover experiments; power and EMI engineers place RL snubbers and choke filters against known noise bands; firmware teams convert millihenry BOM lines into hertz before writing control loops. This RL filter cutoff calculator accepts positive finite resistance and inductance, runs a deterministic multiply-and-divide path, and returns cleaned inputs, fc, omega-c, tau, and a printable expression. Zero resistance is rejected with a clear validation error because the corner formula and tau both require a positive R; zero or negative inductance is likewise invalid.

How the first-order RL cutoff frequency works

A first-order RL network has a single energy-storage element and therefore a single time constant tau equal to L divided by R. The transfer function magnitude reaches one over root two of its passband asymptote at the angular frequency omega-c equal to one over tau, which is R over L. Converting to ordinary frequency in hertz multiplies by one over two pi, so the design equation written on every exam sheet is fc equals R over two pi L.

The low-pass topology places the inductor in series with the load and the resistor as the shunt (or equivalent source resistance), attenuating high frequencies; the high-pass topology swaps the roles and attenuates low frequencies. In both cases the magnitude of the corner is the same product of R and L, which is why a single calculator serves both topologies when the question is only where the three-decibel point sits.

Resistance must be in ohms and inductance in henries so that fc lands in hertz: one thousand ohms with one millihenry yields about one hundred fifty-nine kilohertz, and one ohm with one henry yields about zero point one five nine hertz. Real inductors have series resistance, core loss, and parasitic capacitance that shift the effective corner and roll-off slope, but the first design step is still the ideal formula from the datasheet R and L.

Capacitive reactance, RC time constants, multi-pole ladders, and full Bode plots are different search intents and belong on separate landings so this page stays focused on the RL corner.

Where RL filter cutoff calculators show up in real work

Introductory electronics and signals labs assign RL low-pass and high-pass drills so students convert datasheet ohms and henries into a predicted three-decibel frequency before they measure with a function generator and scope. Audio and instrument designers size series inductors and load resistances for simple passive crossovers and RF chokes by locking fc to a known band edge and then verifying with a network analyzer. Power electronics and EMI teams estimate choke and snubber corners against switching harmonics, using the same R and L product that appears in the control notebook.

Keep RC time-constant, capacitive-reactance, and multi-pole filter landings separate so each search intent has one clear page rather than an overloaded multi-formula tool that confuses both students and search engines.