10Log(Amp Power) = SPL - Sens - 6 + 20*log(Distance to the speaker)
Sound Pressure Level (dB) you like at your listening position
W: Distance between 2 loudspeakers
D: Distance between your position to the center of 2 speakers
Distance to the speaker:
Your position to one of speaker
How Much Amplifier Power Is Needed?
For amplifier pairing, the calculator above gives the minimum amount of wattage required to drive the loudspeakers. The key equation employed by the algorithm is:
SPL = Sens - 20 Log( Meter Distance to one speaker) + 10 Log(Power Watt) +6
Where Sens: Loudspeaker Sensitivity = Sound Pressure measured one meter from the speaker when driven by one Watt of power. And because there are 2 speakers, the intensity is doubled and 6dB added to the total.
Whenever Amplifier power is doubled, SPL increases by 3dB
Whenever Distance is doubled, SPL decreases by 6 dB
An 88dB/1W/1m sensitivity speaker like the W5-1880-SP full range driver, driven by 1 Watt Amplifier power, will result in 88dB SPL measured at one meter distance. When the same speaker is driven by 2 Watts, the SPL will be 91dB (SPL adds 3dB when the power is doubled.). Driven by 4 Watts, the SPL will be 94dB, and so on. If it is driven by 8 Watts at 2 meters, the SPL will be 91dB (= 94 + 3dB due to doubled power – 6dB due to doubled distance).
Let’s take another example. Imagine a 200W x 2 Solid-State amplifier with a pair of bookshelf loudspeakers (sensitivity: 91 dB/1W/1m) operating in a room four meters by five meters. What will the SPL system deliver in this case?
We must first clarify the term ‘Distance’: Here, distance refers to the distance from the listening position to the loudspeakers — the size of the room is irrelevant. So, if the distance to the speaker is 5 meters, then the SPL is 106 dB.
Is this level too big? Too small? For long-term, comfortable listening, 90dB SPL suits most listeners whereas 106dB is not sustainable. This is why some audiophiles love low power, as with delicate Single-Ended Tube amplifiers like EL34-10W paired with higher sensitivity speakers like the W5-1880-SP full ranger with 88 dB sensitivity for living rooms, or paired with 84dB sensitivity 2-way LS35-SP speakers for smaller rooms.
The SE Class A EL34-10W amplifier with a pair of W5-1880-SP bookshelf speakers can provide 95dB SPL @3 meter away. It is more than enough.
Note: Room size and decoration materials affect the music reverberation time and the reflective sound wave. The calculator only considers and calculates the direct sound level to the listener. For the impact of room size and materials, please go to the other “Home effect calculator” for reverberation influence.
Other factors may affect optimum amplifier power: the sensitivity of the listener’s ears for example or their tolerance of distortion, the dynamic of the tracks you're listening to, the acoustics (including the absorber, diffuser, and reverberation in your room), and psychoacoustics. And the unavoidable fact that our ears do not hear exactly the same sound when responding to bass and high frequency. Also, speakers' impedance varies according to changes in frequency. We'll try to elaborate more in the FAQ session.
Frequently asked questions
How much SPL do I need?
How the Human Ears "hear" sound?
The chart shows that the human ear is most sensitive at 3-4 Khz or whistle register in the vocal range and doesn't have to be loud to be heard. In the orchestral range, we hear around the 45-17Khz range. So, when choosing an amplifier or speakers, a smoother frequency response and lower distortion (THD) of this range (45 Hz -20 Khz) should be your most important considerations.
Why bigger power of Solid-State Amplifier is required than Tube Amplifier?
For SS amps to achieve high efficiency levels, a feedback circuit is designed to have the output impedance as low to 0.1 Ohm so as to have most of the power applied to the speaker load efficiently.
Then when the impedance rises to 32 Ohm, the output power is only 1/4 of output power @8 Ohm. So to match the output requires 4 times as much power.
SS amps usually trigger hard clipping when driving over the amplifier’s power rating (overdrive). This hard clipping of sound waves generates a high amplitude of high frequency harmonics that is painful on the ears. So it's better to choose a higher rated power SS amp to make sure you have some more room before hitting the hard clipping point.
Yet in tube amps, which have important soft clipping characteristics, generating lower amplitudes of high frequency harmonics makes for a warmer sound which our ears are more tolerant of. We will elaborate more on next topic.
Can I use 250W or even higher power Amplifier to drive peak power 200W speakers?
Yes. In fact this is something that we highly recommend.
250W is the power measured under 10% distortion, so it can deliver much less distorted power to 200W rated speakers. High quality speakers such as the M1, AP1 and LS35-SP can usually handle more transient power than listed.
Can 30W Amplifier delivers 60W power?
How come the Calculator didn't consider "headroom" factor in Amp power calculation?
For high-end amplifier makers, the maximum power can sometimes be up to 10 times of RMS power listed in the spec, which also means the RMS power marked on the Amplifier is the power needed for your music, with headroom already factored in. To avoid confusing the customer we didn’t consider headroom.
Yet, if you’re looking for an entry-level amplifier from no brand, you can consider adding a headroom factor, or simply double/triple the power in case you purchase the Peak Power instead of RMS power.