Decibel Power Ratio Calculator
Solve the logarithmic decibel equation. Enter any two of dB, P₁ (reference) and P₂ (measured) — the third is calculated instantly with linear ratio, amplitude equivalent and a live power-gain gauge.
dB = 10 · log₁₀(P₂ / P₁)
P₂ = P₁ · 10(dB / 10)
P₁ = P₂ / 10(dB / 10)
dB = 20 · log₁₀(V₂ / V₁) — for field quantities
The factor of 10 applies because decibels are defined for power ratios. When measuring amplitude (voltage, current, sound pressure), the correct factor is 20 because power is proportional to the square of amplitude. This calculator is a power calculator — for amplitude use 20·log₁₀.
| dB | Power ratio | Amplitude ratio | Context |
|---|
The same dB value represents a different amplitude ratio than power ratio — power ratio = 10(dB/10), amplitude ratio = 10(dB/20). This is why the same "3 dB" means ×2 in power but only ×1.41 in voltage. Your current dB is highlighted.
| Unit | Reference | Formula | Typical use |
|---|
A bare "dB" is a dimensionless ratio; adding a suffix makes it absolute — dBm (1 mW), dBW (1 W), dBµW (1 µW), dBV (1 V), dBSPL (20 µPa). The suffix is not decoration; it defines the reference power the dB value is measured against.
| Stages | Cumulative dB | Cumulative power ratio | Output (from P₁) | Notes |
|---|
Decibels add across cascaded stages. Two amplifiers of +10 dB each give +20 dB total (×100 power). One amplifier +10 dB followed by an attenuator −3 dB gives +7 dB. This is the single most useful property of the dB scale.
10·log vs 20·log
Use 10·log₁₀ for power ratios (watts, mW, dBm). Use 20·log₁₀ for amplitude ratios (voltage, current, sound pressure). The factor of two accounts for P ∝ V² — the same physical ratio gives the same dB either way.
dB adds across stages
Multiply in linear, add in dB. A system with +20 dB gain and −3 dB loss has a net +17 dB. This is why link budgets are always drawn in dB — the entire chain is a simple sum.
The 3 dB rule
A 3 dB change is a factor of two in power (100.3 ≈ 2), or a factor of √2 ≈ 1.41 in amplitude (voltage). It is the standard definition of the half-power bandwidth of any filter or antenna.
Suffixes matter
"20 dB" is a ratio. "20 dBm" is an absolute power of 100 mW. "20 dBW" is 100 W. Same number, wildly different meaning. Always check the suffix before interpreting a dB value in a real system.
The decibel equation has three quantities and one relationship. Enter any two and the third is solved instantly, along with linear ratio, amplitude equivalent and absolute reference values.
Choose what to solve for
Common cases: enter P₁ and P₂ to find the dB gain or loss; enter P₁ and target dB to find the required P₂; enter P₂ and target dB to find the required P₁. Use the reference-mode pills to compute absolute power levels (dBm, dBW, dBµW).
Enter the two known values
Type a number, drag the slider, or tap a preset. Each power field has its own unit dropdown — W, mW, µW, nW, kW or hp. The dB field is dimensionless with a −300 to +300 range.
Click Calculate
The page smoothly scrolls to the result card, which flashes briefly. The power-gain gauge animates to show the ratio between P₂ and P₁ on a dB scale from −30 to +30 dB.
Read the power gauge
Values above zero (teal) mean power gain. Values below zero (amber/red) mean power loss. ±3 dB is ×2 / ÷2, ±10 dB is ×10 / ÷10, ±20 dB is ×100 / ÷100.
Use the reference mode
The reference-mode pills fix P₁ to a standard reference (1 mW for dBm, 1 W for dBW, 1 µW for dBµW) so the dB value is an absolute power level rather than a ratio. This is how RF engineers read power measurements.
Advanced mode
Unlocks the application presets (line amp, attenuator, Wi-Fi TX, fiber span, antenna gain, etc.), the cascade table, sensitivity analysis and companion metrics including dBm, dBW and dBµW conversions of your power values.
Three-way solve
Solve for dB, P₂ or P₁ from the other two. The dB solve is a logarithm; the P solves are exponentials. All three are exact.
Live power gauge
A −30 to +30 dB gauge showing P₂/P₁ on a logarithmic scale — the canonical way to visualize a power ratio in signal-chain work.
Three interactive charts
The dB ladder showing common reference points, the full dB-versus-ratio curve on a semi-log axis, and a horizontal application comparison chart.
Companion quantities
Linear power ratio, amplitude ratio, dBm/dBW/dBµW equivalents of P₁ and P₂, doubling count (how many 3 dB steps), decibel-per-octave equivalent, and cascade sum.
Reference tables
Full dB-to-ratio conversion table (power and amplitude), the decibel reference unit table (dBm, dBW, dBµW, dBV, dBSPL), and a cascade table showing cumulative dB across up to 20 stages.
Reference mode
One click sets P₁ to the standard dBm, dBW or dBµW reference so dB becomes an absolute power level — the way it is used in RF and audio engineering.
The decibel is a logarithmic unit used to express the ratio of two quantities — most commonly powers. It is defined as dB = 10·log₁₀(P₂/P₁), so a ratio of 2 corresponds to about 3.01 dB, a ratio of 10 to exactly 10 dB, and a ratio of 100 to 20 dB. The logarithmic scale is not arbitrary: human hearing, electronic gain chains and RF link budgets all span many orders of magnitude, and dB compresses those ranges into manageable numbers while turning multiplication into addition. Two amplifiers with gains of 20 dB and 15 dB in series give a net gain of 35 dB, whereas the linear ratios (100 and 31.6) would require multiplication to 3160. Because power is proportional to the square of amplitude (P = V²/R), the same dB scale applies to amplitude ratios using the factor 20 instead of 10: a voltage ratio of 10 is 20·log₁₀(10) = 20 dB, the same as a power ratio of 100. This is why the 10·log form is used for power and the 20·log form for voltage, current and sound pressure. A bare "dB" is a pure ratio — dimensionless. Add a suffix to make it absolute: dBm references 1 mW, dBW references 1 W, dBµW references 1 µW, dBV references 1 V, and dBSPL references 20 µPa (the threshold of human hearing). The suffix is not decoration; without it, a dB value has no physical meaning.
Because decibels for power use the factor 10, and decibels for amplitude (voltage, current, sound pressure) use the factor 20. The two formulas give the same result for the same physical situation, because power is proportional to the square of amplitude: P = V²/R. So a voltage ratio of 10 gives a power ratio of 100, and 20·log₁₀(10) = 10·log₁₀(100) = 20 dB. This calculator is a power calculator, so it uses the 10·log form. If you have a voltage measurement and want dB, use 20·log₁₀(V₂/V₁) instead.
dB is a dimensionless ratio — it only makes sense when both P₁ and P₂ are specified. dBm is an absolute power level referenced to 1 mW: P(dBm) = 10·log₁₀(P / 1 mW). So 0 dBm = 1 mW, 10 dBm = 10 mW, 30 dBm = 1 W, −30 dBm = 1 µW. In RF work, "the transmitter puts out 20 dBm" means 100 mW of absolute power, not a ratio. If you don't specify the reference, a bare dB value has no physical meaning.
Because 10·log₁₀(2) = 3.0103 ≈ 3. This is the single most useful rule in the field: a 3 dB change is a doubling (or halving) of power. Two 3 dB steps give ×4 (6 dB); three give ×8 (9 dB); ten give ×1024 (30 dB). The 3 dB point is also the standard definition of the half-power bandwidth of any filter or antenna — the frequency at which output power falls to half its peak. The 3 dB rule is not exact (3.0103 vs 3) but the 0.3% error is negligible in practice.
Simply add them. Gains are positive, losses are negative, and the total is the algebraic sum. A receiver front-end might have +20 dB from the LNA, −3 dB from a filter, +15 dB from a mixer stage, and −1 dB from a connector — total +31 dB. In linear terms this would require multiplying 100 × 0.5 × 31.6 × 0.79, which is why every RF engineer works in dB. The cascade table in Advanced mode shows this for your current dB value across up to 20 identical stages.
Yes — negative dB simply means P₂ is less than P₁, i.e., a power loss. An attenuator with −20 dB reduces power by a factor of 100. A long cable with −3 dB loses half the signal. A bare dB value of 0 means P₂ = P₁ (unity, no gain or loss). Because dB is a ratio, there is no "absolute floor" — negative dB just means the output is smaller than the input. Note that negative dB can still correspond to a positive absolute power: −10 dBm is 0.1 mW, which is a positive physical power.
dBi is the gain of an antenna referenced to an ideal isotropic radiator — a hypothetical point source that radiates equally in all directions. An antenna with 10 dBi gain concentrates ten times more power in its main beam than the isotropic reference would in the same direction. dBd references a half-wave dipole instead, which has 2.15 dBi of gain, so dBd = dBi − 2.15. Like dBm, the suffix tells you what the reference is — without it, the number has no absolute meaning. Antenna gain is fundamentally a ratio of power densities, so the 10·log form applies.
What it means
The decibel (dB) is a logarithmic unit used to express the ratio of two powers. For a power ratio P₂/P₁, the value in dB is 10·log₁₀(P₂/P₁). A 10 dB increase means 10 times more power, 20 dB means 100 times, and 3 dB means approximately double. The dB scale is convenient for handling large dynamic ranges, such as audio levels, signal strengths, and gains. It is used in acoustics, telecommunications, and audio engineering. Example: If an amplifier output is 100W and the input is 1W, the gain is 10·log₁₀(100/1) = 20 dB. A loss of 3 dB corresponds to a power ratio of 0.5 (half power), which is common in filters at the cutoff frequency.
Worked example
Decibel Power Ratio – Practical Example
Real‑World| Parameter | Value |
|---|---|
| P1 | 1 W |
| P2 | 100 W |
| Formula | dB = 10·log₁₀(P₂/P₁) |
Common mistakes
Watch unit consistency and the assumptions behind the formula; misapplying it outside its valid conditions is the most frequent error.Applications
The decibel (dB) for power ratio is 10·log₁₀(P₂/P₁), expressing power changes on a logarithmic scale. It is used throughout electrical engineering to describe gains, losses, and signal levels. Engineers use dB to compare amplifier gains, to specify attenuator losses, and to measure signal‑to‑noise ratios. The logarithmic scale compresses wide ranges into manageable numbers, making it easier to work with signals. Understanding dB is essential for RF, audio, and telecommunications engineering.
- Amplifier gain and attenuator loss specification
- Signal‑to‑noise ratio and dynamic range measurement
- Power budget analysis in communication systems
- Audio and RF level metering
- Educational understanding of logarithmic units
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