Calculate original or reduced power with the 3dB rule, converting between watts, kilowatts, and horsepower to find the missing value.
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3dB Rule Formula
The 3dB rule for power says that a 3 dB reduction cuts power by a factor of 103/10, which is about 1.9953. In practical use, this is often rounded to one-half power.
P_2 = \frac{P_1}{10^{3/10}}P_1 = P_2 \times 10^{3/10}- P1 = original power before the 3 dB reduction
- P2 = power after the 3 dB reduction
- 103/10 = 3 dB power ratio, approximately 1.9953
If you enter the original power, the calculator divides it by 103/10 to find the power after a 3 dB reduction. If you enter the reduced power, it multiplies that value by 103/10 to recover the original power.
The calculator also converts between watts, kilowatts, and horsepower before applying the 3 dB rule. It uses watts as the base unit, with 1 kW = 1000 W and 1 hp = 745.7 W.
3 dB Power Change Reference
Use this table to understand common decibel changes for power ratios.
| Change | Power Ratio | Meaning |
|---|---|---|
| -3 dB | 1 / 1.9953 | Power is reduced to about 50.1% |
| +3 dB | 1.9953 | Power is almost doubled |
| -6 dB | 1 / 3.9811 | Power is reduced to about one-quarter |
| +10 dB | 10 | Power is increased by 10 times |
Power Unit Conversions
| Unit | Equivalent in Watts |
|---|---|
| 1 W | 1 W |
| 1 kW | 1000 W |
| 1 hp | 745.7 W |
Example Problems
Example 1: Find power after a 3 dB reduction
You have an original power of 100 W.
P_2 = \frac{100}{10^{3/10}}P_2 \approx 50.1187\text{ W}After a 3 dB reduction, 100 W becomes about 50.1187 W.
Example 2: Find original power from reduced power
You have 2 kW after a 3 dB reduction.
P_1 = 2 \times 10^{3/10}P_1 \approx 3.9905\text{ kW}The original power was about 3.9905 kW.
FAQ
Does a 3 dB reduction always mean exactly half power?
Not exactly. A 3 dB reduction gives a power ratio of 1 / 103/10, which is about 0.5012. That is very close to half, so it is commonly described as half power, but the exact value is slightly above 50%.
Why does the calculator use 10 instead of 20 in the decibel formula?
This calculator is for power. Power ratios use 10log10(P2/P1). The factor 20 is used for field quantities such as voltage, pressure, or amplitude when the impedance or reference conditions are the same.
Can you mix units such as watts and horsepower?
Yes. You can enter one value in watts, kilowatts, or horsepower and choose a different unit for the missing value. The calculation converts the entered value to watts, applies the 3 dB rule, then converts the result into the selected output unit.
