Crossover Slope Calculator

Key Takeaways

Each filter order adds 6 dB/octave of attenuation: 6, 12, 18, or 24 dB/octave for 1st–4th order.
Linkwitz-Riley sums flat on-axis (−6 dB at crossover); Butterworth sums with a +3 dB bump; Bessel preserves transient timing best.
A 2nd-order (12 dB/octave) filter shifts phase 180° — reverse the tweeter's polarity to compensate.
Electrical slope ≠ acoustic slope: a driver's natural roll-off adds to your filter's slope.
Steeper is not free — steep slopes increase group delay and can smear percussive attacks.

What Is a Crossover Slope?

Definition: A crossover slope is the rate at which a crossover filter reduces signal level beyond a speaker driver's intended frequency range, measured in decibels per octave (dB/octave). A steeper slope silences out-of-band sound faster, protecting drivers and reducing interference between woofer and tweeter.

In a 2-way speaker, the woofer and tweeter don't hand off cleanly at one frequency — they overlap across a band where both play at once. The slope controls how wide that overlap band is. A gentle 6 dB/octave slope leaves a wide overlap (more interaction, less protection); a steep 24 dB/octave slope narrows it to a thin slice (maximum isolation, but more phase shift).

Slopes come in standard steps because each reactive component — one inductor or one capacitor — contributes exactly one filter order, and each order contributes 6.02 dB/octave. So a 2nd-order network (one L + one C) gives 12 dB/octave, a 4th-order network gives 24 dB/octave, and so on.

How This Calculator Works

This calculator sizes the reactive components for a 2nd-order (12 dB/octave) crossover section, then scales the values for your chosen filter alignment. It computes the low-pass (woofer) inductor and capacitor and the high-pass (tweeter) capacitor and inductor from your crossover frequency and nominal speaker impedance.

Methodology: base values come from the 1st-order relations C = 1 / (2π·fc·R) and L = R / (2π·fc). For Linkwitz-Riley, both values are multiplied by √2 (≈1.414) to account for the cascaded Butterworth sections; for Bessel, a ×1.2 factor approximates the Bessel coefficient set. We verified this calculator's output against the standard textbook formulas using 5 sample inputs (1–5 kHz at 4 and 8 Ω); results match to within component rounding.

The model assumes ideal components and a resistive load. Real drivers have rising impedance with frequency (voice-coil inductance), which is why designers often add a Zobel network to flatten impedance before the crossover sees it.

Formula + Worked Example

The attenuation of any crossover filter follows one master equation:

Attenuation (dB) = 20 × N × log₁₀(f / fc)

N = filter order, f = frequency of interest, fc = crossover frequency.

Worked example: design a 2nd-order (12 dB/octave) crossover at fc = 3,000 Hz for an 8 Ω driver.

Compute angular frequency: ω = 2π × 3,000 = 18,850 rad/s.
Capacitor: C = 1 / (ω × R) = 1 / (18,850 × 8) = 6.63 × 10⁻⁶ F = 6.63 µF.
Inductor: L = R / ω = 8 / 18,850 = 4.24 × 10⁻⁴ H = 0.42 mH.
Check attenuation one octave up (6,000 Hz): 20 × 2 × log₁₀(2) = 12.04 dB — exactly the 12 dB/octave rating.
For Linkwitz-Riley, scale up: 6.63 × 1.414 = 9.38 µF, 0.42 × 1.414 = 0.60 mH.

How to Use This Calculator

Enter the crossover frequency
Type fc in Hz — typically 2,000–3,500 Hz for a 2-way bookshelf speaker. Use our crossover frequency calculator if you haven't chosen one yet.
Select speaker impedance
Pick the driver's nominal impedance (4, 6, 8, or 16 Ω) from the spec sheet.
Choose the filter alignment
Butterworth for general use, Linkwitz-Riley for the flattest summed response, Bessel for the cleanest transients.
Read the component values
The tool shows low-pass (woofer) and high-pass (tweeter) inductor (mH) and capacitor (µF) values, plus the slope's roll-off, recommended use, and phase behavior.

Reading Your Result

The calculator outputs a 12 dB/octave (2nd-order) design scaled to your chosen alignment. Use this table to judge whether the result fits your build:

Slope	Overlap width	Tweeter protection	Phase at fc	Safe next step
6 dB/oct (1st)	Wide (~3.3 octaves)	Poor — bass reaches the dome	90°	Use only with rugged drivers; add a steeper high-pass for tweeter safety.
12 dB/oct (2nd)	Moderate (~1.7 octaves)	Good for moderate levels	180° — reverse tweeter polarity	This calculator's output: verify polarity with a phase check.
18 dB/oct (3rd)	Narrow (~1.1 octaves)	High	270°	Good compromise; mind the extra parts cost and group delay.
24 dB/oct (4th)	Very narrow (~0.8 octaves)	Maximum	360° — in phase	Best isolation; consider Linkwitz-Riley for flat summation.

Why Exactly 6.02 dB Per Order?

One octave means doubling the frequency, and the decibel math for a voltage ratio is 20 × log₁₀(ratio). Plug in a ratio of 2: 20 × log₁₀(2) = 20 × 0.3010 = 6.02 dB. That's it — one filter order rolls off one "factor of 2" per octave, which is always 6.02 dB.

A 1st-order filter is one reactive element, so it gives 6.02 dB/octave. Stack two elements (2nd order) and the attenuations multiply: 6.02 + 6.02 = 12.04 dB/octave. This is also why engineers sometimes quote dB per decade: one decade is ~3.32 octaves, so 20 dB/decade is the same thing as 6 dB/octave.

Electrical Slope Is Not Acoustic Slope

Here's the concept most calculator pages skip: your filter's electrical slope adds to the driver's natural acoustic roll-off. A woofer already rolling off at 12 dB/octave acoustically, fed through a 12 dB/octave electrical low-pass, produces a 24 dB/octave acoustic slope.

Experienced designers exploit this with asymmetric crossovers: for example, a 2nd-order electrical low-pass on a woofer with a natural 2nd-order roll-off yields a 4th-order acoustic slope — which pairs perfectly with a 4th-order electrical high-pass on the tweeter. If you ignore the driver's own roll-off, your "12 dB" crossover may actually be behaving like an 18 or 24 dB one, with unexpected phase consequences.

Phase and Polarity Cheat Sheet

Every filter order rotates phase by 90°. At the crossover point, the two drivers must arrive in phase or they partially cancel. Use this table when wiring:

Order	Slope	Phase shift	Tweeter wiring
1st	6 dB/oct	90°	Normal polarity
2nd	12 dB/oct	180°	Reversed polarity
3rd	18 dB/oct	270° (≡ −90°)	Normal polarity (verify by measurement)
4th	24 dB/oct	360°	Normal polarity — back in phase

The 2nd-order case catches the most builders: wire the tweeter normally and you get a deep null at the crossover frequency instead of a smooth handoff. When in doubt, measure with a microphone or listen for the hollow "out of phase" sound on pink noise.

When a Steep Slope Hurts: Group Delay

Steeper slopes are not free. Each filter order adds group delay — different frequencies exit the filter at slightly different times. A 4th-order filter delays bass noticeably more than treble, which can smear the attack of kick drums and bass guitar.

This is exactly why the Bessel alignment exists: it sacrifices a sharp cutoff knee for maximally flat group delay, keeping all frequencies time-aligned. For studio monitors and audiophile builds where transient accuracy matters more than ultimate driver isolation, Bessel (or a gentler slope) often sounds more natural than a steep Linkwitz-Riley.

LR2 vs LR4: Specify the Order

"Linkwitz-Riley" alone doesn't tell you the slope. LR2 is the 12 dB/octave version (two cascaded 1st-order Butterworths); LR4 is the 24 dB/octave version (two cascaded 2nd-order Butterworths) and the one most people mean. Both share the signature −6 dB point at fc and flat acoustic summation — they differ only in steepness, phase rotation, and parts count. When following a design or forum advice, always confirm which one is meant.

Crossover Slope Comparison: Which Filter to Use

Alignment	At fc	Summation	Phase behavior	Use when…
Butterworth	−3 dB	+3 dB bump on-axis	Standard rotation	You want maximum simplicity and efficiency; car audio and PA.
Linkwitz-Riley	−6 dB	Perfectly flat	In-phase (even orders)	Flat on-axis response matters most; studio monitors, hi-fi.
Bessel	−3 dB	Slight dip, wide knee	Linear phase, minimal ringing	Transient accuracy matters most; percussive music, audiophile builds.

Limitations

Ideal components assumed. Real inductors have DC resistance and real capacitors have tolerance (±5–10%), both of which shift fc and Q.
Resistive load assumed. A driver's impedance rises with frequency due to voice-coil inductance; without impedance flattening (see Zobel network), actual slopes deviate from the model.
Driver acoustic roll-off ignored. As explained above, the real acoustic slope is electrical + natural — always steeper than this calculator shows.
No baffle or room effects. Baffle step, diffraction, and room reflections reshape the final in-room response.

These are starting-point values for design and simulation. Verify any passive crossover by measuring the finished speaker before committing to expensive components.

Frequently Asked Questions

A crossover slope is how quickly a crossover filter turns down sound outside a driver's range, measured in dB per octave. Common slopes are 6, 12, 18, and 24 dB/octave. Steeper slopes isolate drivers better and protect tweeters from bass, but add more phase shift.

A second-order crossover rolls off at 12 dB per octave (more precisely 12.04 dB). Each filter order contributes 6.02 dB/octave, so two orders give 12 dB. Second-order networks are the most common in passive speaker crossovers because they balance driver protection, parts count, and phase behavior.

Choose Linkwitz-Riley when you want the flattest on-axis response — its −6 dB crossover point lets two in-phase drivers sum perfectly flat. Choose Butterworth for simpler, more efficient designs where a small +3 dB bump at crossover is acceptable, such as car audio. Choose Bessel when transient timing matters most.

With a 2nd-order (12 dB/octave) crossover, yes — the filter shifts phase 180°, so reversing the tweeter's terminals brings the drivers back in phase at the crossover point. With 1st, 3rd, or 4th-order slopes, wire normally. If you're unsure, play pink noise and listen: wrong polarity sounds hollow with a weak center image.

Yes — asymmetric crossovers are standard practice among experienced designers. A common technique pairs a 2nd-order electrical low-pass with a woofer that already rolls off acoustically at 2nd order, creating a 4th-order acoustic slope that mates with a 4th-order electrical high-pass on the tweeter. The goal is matching acoustic slopes, not electrical ones.

A 3rd-order (18 dB/octave) or 4th-order (24 dB/octave) high-pass gives the best tweeter protection, because tweeter excursion rises dramatically as frequency falls. A shallow 6 dB/octave slope lets damaging low-frequency energy reach the dome. For delicate soft-dome tweeters in loud systems, don't go below 18 dB/octave.

Steeper filters introduce more group delay — low frequencies exit the filter later than high frequencies. This time smearing softens the attack of drums and bass transients. Bessel alignments minimize this effect with maximally flat group delay, which is why they're favored for transient-critical studio monitors.

For a 1st-order section: C = 1 / (2π × fc × R) farads and L = R / (2π × fc) henries, where fc is the crossover frequency and R is impedance. Example: 3,000 Hz and 8 Ω gives 6.63 µF and 0.42 mH. For Linkwitz-Riley, multiply both by 1.414. This calculator does the math instantly.

LR2 is the 12 dB/octave Linkwitz-Riley alignment and LR4 is the 24 dB/octave version. Both share the signature −6 dB point at the crossover frequency and flat acoustic summation — the number only specifies steepness. When someone recommends "Linkwitz-Riley," they usually mean LR4; always confirm the order.

A Zobel network flattens a driver's rising high-frequency impedance so the crossover sees the resistive load it was designed for. Without one, actual crossover points and slopes drift from the calculated values — especially with woofers. Use our Zobel network calculator to size it; it's cheap insurance for any passive design.

Speaker Tools

Low-Pass (Woofer)

High-Pass (Tweeter)

Slope Characteristics