Instructions

Why These Calculations Matter

These are not opinions or guesses — they are equations used by audio engineers worldwide. Every step here is based on proven formulas, standard in professional audio design. Follow them, and you’ll design a loudspeaker that works at the highest level.

Woofer Analyzer

The Woofer Analyzer checks the “personality” of your woofer — sensitivity, resonance, and Qts — so you know whether it belongs in a sealed box or a ported one. This ensures your woofer works in harmony with its enclosure.

Formula: Qts = Qes × Qms / (Qes + Qms)

Standard in professional audio design

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Port Length Generator

A port is a resonant pipe. If it’s too short, tuning is too high — bass sounds weak. If it’s too long, it tunes below the woofer’s natural range and adds nothing. The goal is a precise match: box volume, port diameter, and woofer resonance all working together.

Formula: L = (23562.5 × D²) / (V × Fb²) – (0.823 × D)

Standard in professional audio design

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Zobel Network

A woofer’s impedance rises at higher frequencies, confusing the crossover. A Zobel flattens that rise, so the crossover behaves exactly as designed. It’s like adding a shim under a wobbly table leg — the system stabilizes.

Formula: Rz = Re, Cz = Le / Re²

Standard in professional audio design

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Baffle Step Compensation (BSC)

A cabinet boosts the mids while bass wraps around and cancels. BSC corrects that imbalance, making the sound fuller and more natural. Without it: shouty mids. With it: proper bass-to-mid alignment.

Formula: f3 = 4560 / baffle width (in inches)

Standard in professional audio design

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Woofer Crossover

The woofer needs a low-pass filter so it hands off smoothly to the tweeter. Using the right crossover point ensures clarity and prevents distortion. For large woofers (>12"), stay below ~3 kHz for best results.

Formula (1st Order): L = Re / (2πFc)

Formula (2nd Order): L = Re / (2πFc), C = 1 / (2πFcRe)

Standard in professional audio design

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Tweeter Generator

The tweeter handles the highs. Safe crossover points and careful attenuation ensure clarity without harshness or fatigue. This tool sets your tweeter where it performs best.

Formula: Fc = 1 / (2πRC)

Standard in professional audio design

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L-Pad

Tweeters are often more efficient than woofers. An L-pad lowers the tweeter’s output while keeping the load stable, protecting the crossover and ensuring seamless blending.

Formula: Attenuation ≈ 20 × log10(Rs / (Rs + Rp))

Standard in professional audio design

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Speaker Design Instructions

A Proven Formula from Start to Finish

Great speakers aren’t built on hunches — they’re built on equations. The formulas here are not opinions or trends; they are stone-cold facts of physics, developed and refined over decades by renowned audio engineers. Use them, and you’re following the same process that world-class designers use.

1. Woofer Selection

The woofer is your foundation. Its Thiele/Small parameters (sensitivity, Fs, Qts, size) define what kind of enclosure it belongs in. The Woofer Analyzer checks these numbers and tells you if the driver works best in a sealed box (tight bass) or a ported box (deeper bass). Choosing correctly ensures the woofer will deliver stable, low-distortion performance.

2. Box & Port Alignment

The cabinet and port work hand-in-hand with the woofer. If the port is too short, tuning is too high and bass sounds thin. If it’s too long, tuning drops below the woofer’s useful range and adds nothing. The formulas here set the correct box volume and port length so the woofer and enclosure reinforce each other instead of fighting each other.

3. Zobel Network

Woofers naturally rise in impedance at higher frequencies. A Zobel network (capacitor + resistor) flattens that curve, allowing the crossover to behave predictably. Think of it as leveling the playing field so your high-pass and low-pass filters work exactly as designed.

4. Baffle Step Compensation (BSC)

Any woofer in a box radiates bass in all directions but mids straight forward, which makes the midrange sound louder than the bass. BSC uses a coil and resistor to restore balance, so bass and mids are even. Without it, speakers often sound thin or shouty; with it, they sound natural and full.

5. Crossover Integration

The tweeter takes over where the woofer leaves off. Safe crossover points are based on the tweeter’s resonant frequency (Fs) and the manufacturer’s recommended minimum crossover. Our formulas apply a second-order (12 dB/octave) network with reversed polarity at crossover, ensuring smooth phase alignment. For woofers 12″ and larger, avoid very high crossover points — large cones cannot cleanly hand off at 3–4 kHz.

6. L-Pad Attenuation

Tweeters are usually more efficient than woofers. An L-Pad (series + parallel resistor) reduces their level while keeping the impedance stable for the crossover. Raising the parallel resistor brightens the tweeter (less cut); lowering it darkens the tweeter (more cut). This gives you precise control over tonal balance without upsetting the crossover math.

Final Note

These calculations are historically proven, mathematically exact, and universally accepted in audio design. They don’t guess, and they don’t change with trends. Follow them, and you’re not experimenting — you’re building on a proven, professional foundation.

Note: These results are intended as guidance for precise tuning (especially for critical audio applications or complex enclosures)

we recommend using dedicated speaker design software such as

WinISD, VituixCAD, HornResp, BassBox Pro, or SpeakerSim.

Shinjitsu Audio

Note: These results are intended as guidance

for precise tuning (especially for critical audio applications or complex enclosures)

we recommend using dedicated speaker design software such as

WinISD, VituixCAD, HornResp, BassBox Pro, or SpeakerSim.

Shinjitsu Audio