The speaker crossover calculator above produces the component values for a passive two-way network: the low-pass section that feeds the woofer and the high-pass section that feeds the tweeter, both centred on the crossover frequency you choose. It asks for the alignment as well as the order, because those are two separate choices and only naming both makes the numbers meaningful. A second-order Butterworth and a second-order Linkwitz-Riley have the same 12 dB per octave slope and different component values.
Arb Digital publishes free engineering calculators that state their assumptions in the open. The assumption here is a purely resistive load at the design impedance, which is what every published crossover table assumes and what no loudspeaker driver actually presents. The page treats that as the headline caveat rather than a footnote, because it is the reason so many home-built networks measure nothing like the design.
What This Speaker Crossover Calculator Does
The hero figure is the first series inductor in the woofer's low-pass branch, which is the component every network of second order or higher has. Below it the note lists every component in both branches with its position, because a third- or fourth-order network is a ladder and the order of the parts matters as much as their values.
The grid gives the tweeter's first series capacitor, the ideal slope in decibels per octave, the level each branch sits at when the signal is exactly at the crossover frequency, and the tweeter's attenuation at whatever test frequency you enter. That last figure is the practical one: it tells you how much protection a tweeter is getting an octave or two below the crossover, which is where tweeters are damaged.
How to Use It
- Choose the crossover frequency from the drivers, not from taste. It should sit comfortably inside the usable range of both, typically at least an octave above the tweeter's resonance and below where the woofer's response starts breaking up.
- Pick the alignment deliberately. Linkwitz-Riley is the usual choice for a flat summed response with drivers on a common baffle; Butterworth gives a milder in-band ripple trade at second order and a different phase relationship.
- Enter the design impedance each driver actually presents near the crossover, not the number printed on the magnet. These are rarely the same.
- Read the branch level at the crossover. Butterworth branches sit at −3 dB there and Linkwitz-Riley at −6 dB, which is the whole reason the two sum differently.
- Use the test frequency to check tweeter protection at a frequency where the driver is vulnerable, and treat the answer as an ideal-filter figure rather than a measured one.
The Formula: How Crossover Components Are Calculated
The network is a passive ladder driven by an amplifier treated as an ideal voltage source and terminated in a resistance R. Each alignment corresponds to a normalised polynomial, and matching the ladder's transfer function to that polynomial fixes every element. Writing ω = 2πfc, the low-pass elements come out as L = gR ÷ ω for series inductors and C = g ÷ (ωR) for shunt capacitors, where g is the normalised prototype value for that position. The high-pass branch is the dual: the same positions become C = 1 ÷ (gωR) and L = R ÷ (gω).
The prototype values follow from the target polynomial. Second-order Butterworth has a quality factor of 0.7071, giving g values of 1.4142 and 0.7071. Second-order Linkwitz-Riley has a quality factor of exactly 0.5, giving 2 and 0.5. Third-order Butterworth gives 1.5, 1.3333 and 0.5. Fourth-order Linkwitz-Riley is two cascaded second-order Butterworth sections, so its polynomial is the square of the Butterworth one, and the ladder values work out as 1.8856, 1.5910, 0.9428 and 0.3536. Siegfried Linkwitz's own paper on passive crossover networks for noncoincident drivers in the Journal of the Audio Engineering Society is the primary source for the alignment that carries his name.
The reactances behind all of this are the standard ones for alternating current, set out in LibreTexts' section on RLC series circuits with AC: an inductor's impedance rises with frequency and a capacitor's falls, which is the entire mechanism by which the network sorts the signal.
Work the defaults through by hand. Fourth-order Linkwitz-Riley at 2,500 Hz into 8 Ω gives ω = 15,708 rad/s. The first woofer inductor is 1.8856 × 8 ÷ 15,708 = 9.603 × 10−4 H, or 0.960 mH. The first tweeter capacitor is 1 ÷ (1.8856 × 15,708 × 8) = 4.220 µF. The remaining woofer parts are 12.66 µF, 0.480 mH and 2.814 µF; the remaining tweeter parts are 0.320 mH, 8.441 µF and 1.440 mH. Each branch sits 6.02 dB down at the crossover point, and the ideal fourth-order tweeter response one octave below is 24 dB down.
The Eight-Ohm Assumption Is the Weak Point
Every formula on this page assumes the driver behaves like a resistor of the value you entered. Drivers do not. A moving-coil driver's impedance has a tall peak at its free-air resonance, often several times the nominal figure, and it climbs steadily through the top of its range because the voice coil is an inductor. The nominal impedance printed on a driver is a rough minimum, not a description.
The consequence is not subtle. A filter designed for 8 Ω and connected to a load that is 20 Ω at the frequency in question has an entirely different corner frequency and quality factor from the intended one. The measured acoustic slope through the crossover region is frequently nothing like the paper design, and the summed response develops a dip or a peak that no amount of adjusting component values by ear will resolve.
The standard remedy is to flatten the load before filtering it. A Zobel network across the driver terminals cancels the rising inductive part, and a notch across the resonance tames the peak. With both in place, the driver looks much more like the resistor the formula assumes and the calculated values start to behave. Anyone building a passive network for measured drivers should treat this compensation as part of the design rather than an optional refinement. For the impedance behaviour itself, the RLC impedance calculator shows how the reactances combine, and the inductance converter handles the unit conversions that catch people between millihenries and microhenries.
Choosing Between Butterworth and Linkwitz-Riley
The difference is in what happens at the crossover frequency, where both drivers are producing sound. A Butterworth branch is 3 dB down there, and since the two branches are not perfectly in phase, the acoustic sum rises by about 3 dB through the crossover region — an audible bump on the axis where you listen.
A Linkwitz-Riley branch is 6 dB down at the crossover instead, and the two branches arrive in phase, so they sum to exactly flat. This is why it became the default for studio monitors and for any design where the summed on-axis response is the priority. The fourth-order version is two cascaded second-order Butterworth sections, which is where its polynomial comes from.
There is a cost, and it is physical rather than electrical. Steeper filters need more components, and every inductor has resistance that eats power and every capacitor has tolerance that moves the corner. A first-order network uses one part per branch and has the gentlest phase behaviour of all, but it leaves the tweeter exposed to a great deal of low-frequency energy, which is why it is rare in anything that plays loudly. The general filter behaviour behind all of these is covered by the filter cutoff calculator, which handles generic RC, RL and LC topologies rather than multi-way speaker networks.
What the Calculator Deliberately Does Not Do
It does not model the drivers, the baffle or the room, and those three between them usually dominate the result. The acoustic response you hear is the electrical filter response multiplied by the driver's own response, and a tweeter that is already rolling off naturally near the crossover adds its own slope on top of the filter's.
It does not account for acoustic offset either. Unless the two drivers' acoustic centres line up, sound from one arrives slightly later than the other, which shifts the phase relationship at the crossover and changes how the branches sum. This is why sloped baffles and stepped fronts exist, and why a network that measures well flat on a bench can misbehave once the drivers are mounted.
It also says nothing about level matching. Tweeters are usually more sensitive than woofers, so a network with no attenuation on the tweeter gives a bright, thin balance regardless of how correct the filter is. Attenuation is normally handled by a resistive pad, which also alters the impedance the filter sees — another reason the two problems have to be solved together. The Ohm's law calculator covers the resistor arithmetic for that pad.
Where This Page Sits Among the Speaker Tools
Building a loudspeaker splits into an acoustic problem and an electrical one, and Arb Digital publishes tools for both sides. The speaker box volume calculator handles the enclosure: gross and net internal volume after driver, port and bracing displacement, and the sealed-box alignment check. The speaker port length calculator tunes a vented enclosure to a chosen frequency. Neither touches a capacitor or an inductor.
This page owns the electrical side and nothing else. It takes the crossover frequency as given, assumes the enclosure is already decided, and produces the network that divides the signal between the drivers. The boundary is clean: cabinet volume and port tuning set what the woofer does acoustically at the bottom of its range, and the crossover sets what each driver is asked to reproduce at the top of its range.
In practice the two interact at one point. The enclosure alignment determines how low the woofer usefully plays and how it behaves near its own resonance, and that resonance is exactly where the driver's impedance peak sits. A crossover branch calculated for a nominal impedance will misbehave near that peak, which is why an enclosure decision made after the network is designed can invalidate it.
Arb Digital builds free tools like this one because useful pages earn attention. If you want tools, calculators or content built for your own audience, we can help.
Browse All Free Tools Talk to Arb DigitalCommon Mistakes to Avoid
- Using the nominal impedance printed on the driver — it is a rough minimum, not the impedance near the crossover frequency, and the difference moves the corner frequency substantially.
- Naming a slope without naming an alignment — second-order Butterworth and second-order Linkwitz-Riley have identical slopes and different component values, so a design described only as twelve decibels per octave is underspecified.
- Crossing too close to the tweeter's resonance — the impedance peak wrecks the filter behaviour there and the driver is mechanically vulnerable, which is where tweeters are usually destroyed.
- Ignoring inductor resistance — a large air-core inductor in series with a woofer has real DC resistance that reduces output and interacts with the driver's damping.
- Treating the electrical slope as the acoustic slope — the driver's own roll-off adds to the filter's, so the measured acoustic slope is usually steeper than the network alone.
Related Free Tools From Arb Digital
The speaker box volume calculator and speaker port length calculator handle the enclosure side of the same build. The decibel calculator converts the attenuation figures here into level ratios. Driver spacing and baffle step depend on wavelength, so the propagation speed matters there too. Everything Arb Digital publishes sits on the free online tools hub.
Frequently Asked Questions
They are different filter alignments, so they give different component values for the same slope. A Butterworth branch is three decibels down at the crossover frequency and the two branches sum to a rise of about three decibels through that region. A Linkwitz-Riley branch is six decibels down and the branches arrive in phase, so they sum flat. That flat summation is why Linkwitz-Riley is the usual default for two-way designs.
Almost always because the driver is not the resistor the formula assumes. Impedance peaks sharply at the driver's resonance and rises steadily at high frequency because of voice-coil inductance, so the actual corner frequency and quality factor differ from the design. Adding a Zobel network to flatten the inductive rise and a notch across the resonance brings the real load closer to the assumption.
It is a trade rather than a ranking. First order uses one component per branch and has the gentlest phase behaviour, but it leaves a tweeter exposed to a lot of low-frequency energy. Fourth order protects the tweeter well and keeps the drivers from overlapping much, at the cost of more components, more inductor resistance and more accumulated phase shift. Second and fourth order Linkwitz-Riley are the common choices in practice.
Comfortably inside the range both drivers handle well, which usually means at least an octave above the tweeter's resonance and below the frequency where the woofer's response starts to break up or beam. The exact figure comes from the two drivers' measured responses and power handling, not from a rule of thumb, because a crossover placed where either driver is already struggling cannot be rescued by the network.
For anything beyond a rough first attempt, yes. The published equations assume a flat resistive load. A Zobel network across the driver cancels the rising inductive component and a parallel notch tames the resonance peak, and with both in place the calculated component values behave much closer to the design intent. Without them, adjusting values by trial and error rarely converges.
It computes one low-pass and one high-pass section at a single frequency, which is a two-way network. A three-way design is usually built as two such crossover points with a band-pass section in the middle, and that middle section's behaviour depends on how far apart the two frequencies are. Running this tool twice gives the outer sections but does not capture the interaction between them.
They solve different halves of the same build. The box volume calculator is enclosure geometry and acoustic alignment: internal volume, displacement deductions and sealed-box behaviour. This page is the electrical network that divides the amplifier's signal between the drivers. Neither one substitutes for the other, and the enclosure decision should be made first because it affects the impedance the crossover sees.
This tool is provided for educational and hobbyist design use. It applies the published passive filter alignments to an idealised resistive load and does not model real driver impedance, acoustic offset, baffle effects or power handling. Verify any finished network by measurement, and treat amplifier and driver power limits as the manufacturer states them.
