Calculate dB gain, final power, or initial power from two known values in W, kW, or HP using the power ratio formula with unit conversion.

dB Gain Calculator

Enter exactly 2 values to calculate the missing variable

dB Gain Formula

The dB gain calculator uses the power-ratio decibel formula. Power values are converted to watts before calculation, then converted back to the selected output unit if needed.

G₍dB) = 10log₁₀((P_f) / (Pᵢ))
P_f = Pᵢ × 10^G₍dB) / 10
Pᵢ = (P_f) / (10^G₍dB) / 10)
  • GdB = gain in decibels, dB
  • Pf = final power
  • Pi = initial power
  • log10 = base-10 logarithm

If you enter final power and initial power, the calculator finds the dB gain. If you enter initial power and dB gain, it finds the final power. If you enter final power and dB gain, it finds the initial power.

The calculator supports power entries in watts, kilowatts, and horsepower. Internally, it converts power to watts using 1 kW = 1000 W and 1 HP = 745.7 W.

Common dB Gain Values for Power Ratios

Use this table to check whether your result is in the expected range.

dB gain Power ratio Meaning
-10 dB 0.1× Final power is one-tenth of initial power
-3 dB About 0.5× About half power
0 dB 1× No gain or loss
3 dB About 2× About double power
10 dB 10× Final power is ten times initial power
20 dB 100× Final power is one hundred times initial power

Power Unit Conversions Used

Unit Equivalent in watts
1 W 1 W
1 kW 1000 W
1 HP 745.7 W

Example Calculations

Example 1: Calculate dB gain

You have an initial power of 5 W and a final power of 50 W.

G₍dB) = 10log₁₀((50) / (5))
G₍dB) = 10log₁₀(10) = 10 dB

The dB gain is 10 dB.

Example 2: Calculate final power

You have an initial power of 20 W and a gain of 3 dB.

P_f = 20 × 10⁽3 / 10)
P_f ≈ 20 × 1.9953 = 39.9052 W

The final power is about 39.9052 W.

FAQ

What does a negative dB gain mean?

A negative dB gain means the final power is lower than the initial power. For example, -3 dB means the final power is about half the initial power, and -10 dB means the final power is one-tenth of the initial power.

Why does the formula use 10 instead of 20?

The calculator compares power values, so it uses 10 log10. The 20 log10 form is used for field quantities such as voltage or current when impedance is the same.

Can initial power be zero?

No. The dB gain formula divides by initial power, so initial power cannot be zero. A zero or negative power value is not valid for this power-ratio decibel calculation.