Speaker Calculators: Box, Port, SPL and Wiring

Wiring

Series & parallel impedance

Work out the load your amplifier sees when you link several drivers or cabinets together.

Impedance of each driver (Ω)

In series per string

Strings in parallel

Example: four WM1850/8 drivers (8 Ω) wired 2 series × 2 parallel

Mixed loads, comma separated (Ω)

Total load: –
Drivers: –
Mixed loads total: –

Series Z = Z₁ + Z₂ + … Parallel 1/Z = 1/Z₁ + 1/Z₂ + … Grid Z = Z_driver × series ÷ parallel

Amplifiers

Amp power vs impedance

An amplifier is a voltage source, so its power changes with the load. Enter the amp's rating at one impedance to see what it delivers into yours.

Amp rating (W per channel)

Rated into (Ω)

Your load (Ω)

Drivers on this channel

Driver power rating (W, AES)

Example: one WM1850/8, 1800 W AES from its spec sheet, on a 2000 W @ 4 Ω amp

Power into your load: –
Per driver: –
Output voltage: –
Amp vs driver rating: –

Load	Ideal power	Current

Ideal figures. Real amps usually give somewhat less than double when the load halves, and many are not stable below 2 Ω. Check the manufacturer's rating for your load.

V = √(P_rated × Z_rated) P = V² ÷ Z_load I = V ÷ Z_load

Level

SPL at distance

Estimate the sound pressure level from a driver's sensitivity, the amp power and how far away the listener is.

Sensitivity (dB 1 W / 1 m)

Power per box (W)

Number of boxes

Listener distance (m)

Boxes stacked together and playing low frequencies (they couple: +6 dB per doubling instead of +3 dB)

Example: WM1850/8, 93.5 dB from its spec sheet, two boxes at 1000 W each

SPL at listener: –
At 1 m: –
Gain from power: –
Gain from boxes: –

Free-field estimate. Real systems lose a few dB to power compression at full power; rooms and ground reflections add level, especially at low frequencies.

SPL = sens + 10·log₁₀(P) − 20·log₁₀(d) + k·log₁₀(N) k = 20 coupled, 10 not

Level

dB addition

Decibels do not add like ordinary numbers. Combine the levels from several boxes, or convert between dB and power or voltage ratios.

Levels to combine (dB)

Same signal, in phase (coherent: adds pressure, +6 dB for two equal sources)

Convert dB

Convert power ratio

Combined level: –
Above loudest: –

3 dB power ratio: –
3 dB voltage ratio: –
Power ratio in dB: –

Incoherent L = 10·log₁₀(Σ 10^(Lᵢ/10)) Coherent L = 20·log₁₀(Σ 10^(Lᵢ/20))

Enclosures

Sealed & vented box designer

Model a driver's low-frequency response, cone excursion, port air speed and impedance from its Thiele/Small parameters. Pick a box volume and tuning, then check the charts.

Driver

Fs (Hz)

Qes

Qms

Vas (L)

Re (Ω)

Sd (cm²)

Xmax (mm)

Le (mH)

Nominal Ω

Net volume (L)

Tuning Fb (Hz)

Total port area (cm²)

Number of ports

Amp power (W)

Subsonic filter

Filter frequency (Hz)

Box losses QL

The WM1850/8 values come from its spec sheet. Box size, tuning, port and power are example choices for you to change. A 600 cm² port is a 400 × 150 mm slot or a 276 mm round tube; length assumes a round port flush with the baffle. The WM18X451 has no published T/S data yet, so use Custom once you have it.

−3 dB point: –
−10 dB point: –
Peak excursion: –
Port air speed: –
Port length: –
Max SPL at 1 m: –

SPL is for the amp power above, at 1 m in half space (box on the ground). Drive voltage = √(power × nominal Ω). The model is a linear small-signal one: it ignores power compression and the voice coil inductance for SPL, so real output at full power will be a little lower.

Enclosures

Port length calculator

Find how long a round or slot port must be to tune a box to a chosen frequency. Works for any driver, no T/S data needed.

Net box volume (L)

Tuning (Hz)

Inside diameter (mm)

Number of ports

Air temp (°C)

Port ends

Length of each port: –
Total port area: –
Port volume to add: –
First pipe resonance: –

A slot port that runs along a cabinet wall behaves a little longer than its physical length, so cut it slightly short and check the tuning with an impedance sweep. Remember to add the port's own volume to the gross box size.

L = c²·S_total ÷ (4π²·Fb²·Vb) − k·r r = √(S_port/π) k = 1.463 flanged + free

Cabling

Speaker cable loss

Long, thin cable wastes amp power and loosens bass control. Check the loss for your run and see which size you need.

Cable run, one way (m)

Conductor size

Load (Ω)

Amp damping factor

Example: two WM1850/8 cabs in parallel (4 Ω) on a 20 m run of 2.5 mm²

Level lost: –
Cable resistance: –
Power wasted: –
Damping at speaker: –

Size	Loop Ω	Loss	Wasted	Damping

R = 2 × length × ρ ÷ area ρ_Cu = 1.724×10⁻⁸ Ω·m loss = 20·log₁₀(Z ÷ (Z + R))

Acoustics

Wavelength vs frequency

Useful for sub spacing, horn path lengths and working out when boxes stop coupling. Quarter-wave spacing is where a reflection or neighbour starts to cancel.

Frequency (Hz)

Air temp (°C)

Speed of sound at this temperature:

Wavelength: –
Half wave: –
Quarter wave: –
Period: –

Frequency	Wavelength	½ wave	¼ wave

λ = c ÷ f c = 331.3 × √(1 + T/273.15) m/s

Reference

Reference tables

The numbers PA engineers look up most often.

Decibels to ratios

dB	Power ratio	Voltage / pressure ratio

+3 dB needs double the amp power. +10 dB needs ten times the power and sounds roughly twice as loud.

Distance loss (inverse square)

Distance	Level change vs 1 m

−6 dB each time the distance doubles, for a single box in free field.

Speaker cable sizes

Size	mm²	Ω/km per core	Max run 8 Ω	Max run 4 Ω

Max run is the one-way length that keeps the loss under 0.5 dB, copper at 20 °C.

Frequency bands

Band	Range	What you hear
Sub bass	20–60 Hz	Felt more than heard. Dub, D&B and 808 subs live here.
Bass	60–250 Hz	Kick punch, bass guitar body, warmth.
Low mids	250–500 Hz	Fullness. Too much sounds muddy or boxy.
Mids	500 Hz–2 kHz	Most instrument and vocal fundamentals.
Upper mids	2–4 kHz	Clarity and bite. The ear is most sensitive here.
Presence	4–6 kHz	Definition and edge on vocals and snare.
Brilliance	6–20 kHz	Cymbals, air and sparkle. Horn and tweeter territory.

Instrument and voice ranges

Source	Fundamental range	Notes
Pipe organ	16 Hz – 8 kHz	32 ft stop reaches C0, 16.4 Hz.
Synth / 808 sub	25 – 60 Hz	Typical sub-bass lines in dub, D&B and hip hop.
Piano	27.5 Hz – 4.19 kHz	A0 to C8.
5-string bass	30.9 – 392 Hz	Low B0 up to G4 at the 24th fret.
4-string bass	41.2 – 392 Hz	Open E1 up to G4 at the 24th fret.
Kick drum	50 – 100 Hz	Beater click sits around 2–5 kHz.
Cello	65.4 Hz – 1 kHz	C2 upward.
Guitar	82.4 Hz – 1.18 kHz	Open E2 to D6 at the 22nd fret.
Bass voice	82 – 330 Hz	E2 to E4 singing range.
Tenor voice	131 – 523 Hz	C3 to C5.
Snare drum	150 – 250 Hz	Body here, snare wires up to 8 kHz and beyond.
Trumpet	165 Hz – 1 kHz	Sounding E3 to around C6.
Alto voice	175 – 698 Hz	F3 to F5.
Violin	196 Hz – 2.6 kHz	G3 to E7.
Soprano voice	262 Hz – 1.05 kHz	C4 to C6.
Cymbals & hi-hat	300 Hz – 15 kHz+	Most energy above 3 kHz.

Fundamentals only. Harmonics run several octaves higher and give each instrument its character.

Speaker maths

Series & parallel impedance

Amp power vs impedance

SPL at distance

dB addition

Sealed & vented box designer

Port length calculator

Speaker cable loss

Wavelength vs frequency

Reference tables

Decibels to ratios

Distance loss (inverse square)

Speaker cable sizes

Frequency bands

Instrument and voice ranges