Amplifier Power Calculator
How many watts a speaker needs to reach a given loudness at a given distance, with the headroom counted in.
Results
Power needed, headroom included
179.57
W
Power needed with no headroom
45.11
W
Loudness this amplifier reaches
98.46
dB
Loudness at one metre
108.00
dB
Lost to distance
9.542
dB
Headroom left over
3.46
dB
Is this amplifier enough?
It reaches the level, but with less headroom
What doubling the power buys
3.01
dB
Voltage across the load
37.902
V
What this tool does
Doubling the power buys three decibels, which is why the last few decibels cost so much: going from 95 to 101 dB needs four times the amplifier. Headroom is the other half of the question — music peaks well above its average level, and an amplifier sized for the average clips on every transient. The page counts both, and says plainly whether the amplifier you have is enough.
Formula
SPL = sensitivity + 10 log₁₀(P) − 20 log₁₀(d) · P = 10^((SPL − sensitivity + 20 log₁₀(d) + headroom) ÷ 10)
Variables
| Symbol | Meaning | Unit |
|---|---|---|
se | Speaker sensitivity, 1 W at 1 m | dB |
sp | Loudness you want | dB |
ds | How far you sit | m |
hr | Headroom you want to keep | dB |
pw | Power the amplifier delivers | W |
PR | Power needed, headroom included | W |
PN | Power needed with no headroom | W |
SM | Loudness this amplifier reaches | dB |
SO | Loudness at one metre | dB |
LO | Lost to distance | dB |
HM | Headroom left over | dB |
EN | Is this amplifier enough? | — |
DB | What doubling the power buys | dB |
VO | Voltage across the load | V |
Worked example
- Speaker sensitivity, 1 W at 1 m88 dB
- Loudness you want95 dB
- How far you sit3 m
- Headroom you want to keep6 dB
- Power the amplifier delivers100 W
- Power needed, headroom included179.57 W
- Power needed with no headroom45.11 W
- Loudness this amplifier reaches98.46 dB
- Loudness at one metre108.00 dB
- Lost to distance9.542 dB
- Headroom left over3.46 dB
- Is this amplifier enough?It reaches the level, but with less headroom
- What doubling the power buys3.01 dB
- Voltage across the load37.902 V
Limitations
- The result is an estimate based only on the values you type. Real situations often include factors this calculator does not know about.
- The calculation runs at full precision and only the display is rounded. If you copy an intermediate value and retype it, small differences can appear.