What impedance an amplifier actually sees
An amplifier does not care how many speakers you connect. It cares about the single impedance presented at its terminals, because that impedance and the output voltage together determine the current the output devices must supply. Halve the load and, for a given voltage, you double the current and double the power dissipated inside the amplifier as well as in the speakers. That is why every amplifier carries a minimum load rating, and why exceeding it is a hardware failure rather than a sonic compromise.
Combining speakers follows the same two rules as any other pair of impedances. In series the same current flows through every speaker, so their impedances add: two 8-ohm cabinets in series present 16 ohms. In parallel every speaker sees the same voltage, so their conductances add and the total falls: two 8-ohm cabinets in parallel present 4 ohms. Series-parallel combines both, which is how a four-driver cabinet is wired to land back on a convenient number.
Rated impedance is a nominal figure, not a measurement. A speaker described as 8 ohms has a DC resistance of about 6 ohms, a resonance peak that may reach 40 ohms or more, and a rising impedance at high frequencies from voice-coil inductance. IEC 60268-5 defines the rated impedance as a nominal value tied to the minimum of the impedance curve above resonance, and it is that nominal value you use for this arithmetic. Measuring a cabinet with a multimeter gives the DC resistance, which is always lower and is not the number to wire from.
Series, parallel and how power divides
Series is addition: Z = Z1 + Z2 + ... For n identical speakers that is simply nZ. Parallel is the reciprocal sum: 1/Z = 1/Z1 + 1/Z2 + ..., which for n identical speakers reduces to Z/n. Series-parallel with b equal branches of n/b speakers gives Z x (n/b) / b - so four 8-ohm drivers in two branches of two give 8 x 2 / 2 = 8 ohms, and four 16-ohm drivers wired the same way give 16 ohms.
Power division is where mixed impedances bite. Speakers in parallel all see the amplifier's output voltage, and P = V2/Z, so the lowest-impedance speaker always takes the most power. Put a 4-ohm and an 8-ohm cabinet in parallel and the 4-ohm one receives exactly twice the power of the 8-ohm one, which is a good way to cook a driver that is not rated for it.
In series the relationship inverts. Every speaker in a chain carries the same current, and P = I2Z, so the highest-impedance speaker dissipates the most power. The same 4-ohm and 8-ohm pair wired in series delivers twice the power to the 8-ohm cabinet. Neither arrangement shares evenly, and the only way to share evenly is to use matched impedances.
To turn impedance into watts you need the amplifier's output voltage, which follows from its published rating: V = sqrt(Prated x Zrated). An amplifier rated 100 W into 8 ohms produces sqrt(800) = 28.28 V at full output. Into 4 ohms that same voltage would give 28.282/4 = 200 W. Real amplifiers never quite double, because the power supply sags under the extra current draw, so treat the doubling as a ceiling. The underlying arithmetic is ordinary Ohm's law, and the Ohm's law calculator and parallel resistance calculator handle the same relationships in a general electrical context.
Worked example: adding an extension cabinet to a 100 W amplifier
You have a combo amplifier rated 100 W into 8 ohms with a stated minimum load of 4 ohms, and an 8-ohm internal speaker. You want to add an 8-ohm extension cabinet through the second jack, which is wired in parallel.
- Total load. 1/Z = 1/8 + 1/8 = 0.25, so Z = 1/0.25 = 4 ohms. That is exactly the amplifier's minimum, so it is legal but with no margin.
- Amplifier voltage. V = sqrt(100 W x 8 ohms) = sqrt(800) = 28.28 V.
- Total power. P = 28.282 / 4 = 800 / 4 = 200 W in the ideal case.
- Per speaker. Both are 8 ohms and both see 28.28 V, so each takes 800/8 = 100 W. Check: 2 x 100 = 200 W, which matches the total.
- Now substitute a 4-ohm extension. 1/Z = 1/8 + 1/4 = 0.375, so Z = 2.67 ohms - below the 4-ohm minimum, so this must not be connected. The 4-ohm cabinet would also take 800/4 = 200 W against the internal speaker's 100 W, twice the share.
- Fix it by rewiring in series. 8 + 4 = 12 ohms, comfortably above the minimum. Total power falls to 800/12 = 66.7 W, and because the current is now common, the 8-ohm cabinet takes 44.4 W against the 4-ohm cabinet's 22.2 W - twice as much, the reverse of the parallel case.
Verify step 6 independently. The chain current is I = 28.28 / 12 = 2.357 A. Then P8 = 2.3572 x 8 = 44.4 W and P4 = 2.3572 x 4 = 22.2 W, and the two sum to 66.7 W, matching the total. Two routes agreeing is the check worth running every time.
Reading the load figure
The first question is binary: is the total at or above the amplifier's minimum? If it is not, do not connect it, whatever the arrangement sounds like at low volume. A solid-state amplifier driven below its minimum load draws current its output devices are not rated for, and protection circuits are not universal. Valve amplifiers behave differently and are mismatched in either direction: the output transformer expects a specific load, and running a 16-ohm cabinet on a 4-ohm tap stresses the transformer and the tubes just as running a 4-ohm cabinet on a 16-ohm tap does. Match the tap to the load, and never run a valve amplifier with no load at all.
The second question is headroom. A load exactly at the minimum leaves nothing for the impedance dip that every real speaker has somewhere in its curve - the nominal figure is a minimum of the curve, and cable resistance, crossover components and multiple cabinets in parallel can bring the actual minimum lower still. If you have the choice, sitting one step above the minimum is the safer engineering decision even though it costs power.
The third question is sharing. Whenever the impedances are not matched, the calculator's per-speaker table shows the split, and the direction depends on the wiring: lowest impedance takes most in parallel, highest impedance takes most in series. Compare each figure against that driver's own power rating rather than against the amplifier's - a 200 W amplifier can destroy a 50 W driver in a parallel pair without ever showing a fault.
Finally, note that a change in load changes level as well as power. Doubling the power delivered raises the acoustic output by about 3 dB if the speakers are equally sensitive, which is a much smaller subjective change than the doubling implies. The decibel addition calculator handles the logarithmic side of that, including what actually happens when you add a second cabinet.
Common speaker wiring arrangements
| Drivers | Wiring | 4 ohm drivers | 8 ohm drivers | 16 ohm drivers |
|---|---|---|---|---|
| 2 | Series | 8 | 16 | 32 |
| 2 | Parallel | 2 | 4 | 8 |
| 3 | Series | 12 | 24 | 48 |
| 3 | Parallel | 1.33 | 2.67 | 5.33 |
| 4 | Series | 16 | 32 | 64 |
| 4 | Parallel | 1 | 2 | 4 |
| 4 | 2 branches of 2 | 4 | 8 | 16 |
| 6 | 3 branches of 2 | 2.67 | 5.33 | 10.67 |
| 8 | 2 branches of 4 | 8 | 16 | 32 |
| 8 | 4 branches of 2 | 2 | 4 | 8 |
All figures in ohms. The 4x12 guitar cabinet is the row for four 16 ohm drivers in parallel, giving 4 ohms, or four 8 ohm drivers in two branches of two, giving 8 ohms - the two standard mono wirings.
Mistakes that damage equipment
- Measuring impedance with a multimeter. A meter reads DC resistance, typically 75-80% of the rated impedance. An 8-ohm cabinet reads about 6 ohms and is still an 8-ohm cabinet.
- Assuming the second speaker jack is series. Extension jacks on combo amplifiers are almost always parallel, which halves the load with a matched cabinet.
- Mixing impedances in parallel and expecting even sharing. The lower-impedance driver always takes more power, in proportion to the impedance ratio.
- Running a valve amplifier into the wrong tap in either direction. Unlike a solid-state amplifier, a valve output stage is stressed by too high a load as well as too low, and by no load at all.
- Ignoring cable resistance on long runs. Twenty metres of thin cable can add a substantial fraction of an ohm, which matters at 2 or 4 ohms and also degrades damping factor.
- Treating the nominal impedance as flat. It is the minimum of a curve that peaks far higher at resonance, so the amplifier's worst moment is not at the number you calculated.
- Comparing per-speaker power to the amplifier rating instead of the driver rating. The driver's own continuous power handling is the limit that matters.
Constant-voltage systems and where this model stops
Everything above assumes a low-impedance system, where the amplifier is a voltage source and the speakers are wired directly across it. That is how instrument, studio and most live systems work. Distributed systems in buildings work differently: a 70-volt or 100-volt line uses a transformer at each loudspeaker to step the voltage down, and you size the system by adding the wattage taps rather than by combining impedances. If your speakers have a tap switch marked in watts, the arithmetic on this page does not apply - add the taps and keep the total below the amplifier's rating.
The constant-voltage assumption behind the power figures is also an idealisation. A real amplifier's power supply sags under load, so a device rated 100 W into 8 ohms typically makes 160 to 180 W into 4 ohms rather than the theoretical 200 W. Class-D amplifiers with regulated supplies come closer to doubling than traditional linear designs. The calculator reports the theoretical figure precisely because it is the upper bound, and because the manufacturer's own 4-ohm rating is the number to trust when you have it.
Impedance also varies with frequency in ways that matter for amplifier stability. A sealed cabinet has one impedance peak at the system resonance; a ported one has two, with a dip between them that can fall below the nominal figure. Crossovers add reactance, and a badly designed one can present a phase angle that makes the load harder to drive than its magnitude suggests. This is why manufacturers specify a minimum impedance rather than a nominal one, and why derating by one step is cheap insurance.
For the general electrical relationships behind all of this, the series resistance calculator and parallel resistance calculator cover the network arithmetic, and the Ohm's law calculator converts between voltage, current, resistance and power directly.