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Watt to dB Converter

Convert any power level — watts, milliwatts, microwatts down to femtowatts — to dBm and dBW. Uses dBW = 10·log₁₀(P) and dBm = dBW + 30. Includes V_rms across 50 Ω, zone classification, and a transmit/receive reference table.

Input

Power

Canonical power: 100 mW

Common Power Levels

Result

Decibels (ref 1 mW)

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dBm

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dBW (ref 1 W)

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Power (auto-scaled)

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V_rms across 50 Ω

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Formulas

dBW = 10 · log₁₀(P / 1 W)

dBm = 10 · log₁₀(P / 1 mW) = dBW + 30

V_rms across 50 Ω = √(P × 50)

P = 0 → −∞ dB ; P < 0 is non-physical.

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Common Power → dB Reference

Power	dBm	dBW	V_rms @ 50 Ω
1 MW	+90 dBm	+60 dBW	~7.07 kV
1 kW	+60 dBm	+30 dBW	~223.6 V
100 W	+50 dBm	+20 dBW	~70.7 V
10 W	+40 dBm	+10 dBW	~22.4 V
1 W	+30 dBm	0 dBW	~7.07 V
100 mW	+20 dBm	−10 dBW	~2.24 V
10 mW	+10 dBm	−20 dBW	~707 mV
1 mW	0 dBm	−30 dBW	~224 mV
100 µW	−10 dBm	−40 dBW	~70.7 mV
1 µW	−30 dBm	−60 dBW	~7.07 mV
1 nW	−60 dBm	−90 dBW	~223.6 µV
1 pW	−90 dBm	−120 dBW	~7.07 µV
1 fW	−120 dBm	−150 dBW	~223.6 nV
0	−∞ dBm	−∞ dBW	0 V

About Power → dB Conversion

Both dBm and dBW are absolute power units — they specify what 0 dB means. 0 dBm = 1 milliwatt, 0 dBW = 1 watt. Because 1 W is exactly 1000 mW (which is 30 dB), the two scales are offset by 30: dBm = dBW + 30. The conversion from linear power uses the ÷10 form: dB = 10·log₁₀(P / P_ref), because dBm and dBW measure power directly (not amplitude, which uses ÷20).

Why the ÷10 (not ÷20)?

Power-based dB scales use ÷10. Amplitude-based scales (dBV, dB SPL, dBu, dBFS) use ÷20. The factor-of-2 difference comes from P ∝ A² — doubling the amplitude quadruples the power, so the same "+6 dB amplitude" only adds 3 dB of power. dBm and dBW are explicitly power references, so they always use ÷10.

What is "V_rms across 50 Ω"?

RF and test-equipment systems are nearly all standardized on a 50-ohm characteristic impedance. Given a power, the equivalent open-circuit RMS voltage across a 50 Ω load is V = √(P × 50). So 1 mW = 0 dBm = ~224 mV_rms into 50 Ω. This is the connection between dBm (used by RF folks) and oscilloscope readings (used by everyone). For 75 Ω (cable TV) or 600 Ω (legacy audio) systems, replace 50 with the appropriate impedance.

Why does P = 0 give −∞ dB?

log₁₀(0) is mathematically undefined — the limit as P → 0⁺ is negative infinity. So absolute zero power is represented as "negative infinity decibels". In practice every system has a thermal noise floor (≈ −174 dBm/Hz at room temperature) below which signals can't be reliably detected. True −∞ dB is only meaningful as a mathematical limit.

Frequently Asked Questions

What is 1 watt in dBm?

1 W = 1000 mW. dBm = 10·log₁₀(1000) = +30 dBm. Equivalently, 1 W = 0 dBW, and adding 30 (the dBm/dBW offset) gives +30 dBm. This is the regulatory cap on US WiFi 2.4 GHz routers (EIRP).

How do I convert milliwatts to dBm quickly?

Exact: dBm = 10·log₁₀(mW). Mental shortcut: each ×10 in power = +10 dB. So 1 mW = 0 dBm, 10 mW = +10 dBm, 100 mW = +20 dBm, 1 W = +30 dBm. For ×2 (doubling), add 3 dB; for ×0.5 (halving), subtract 3 dB. So 200 mW ≈ +23 dBm (20 + 3).

Why are RF receiver sensitivities expressed in negative dBm?

Because the powers involved are tiny — far less than 1 mW (which is 0 dBm). A WiFi receiver might decode signals at −90 dBm, which is 10⁻⁹ mW = 1 pW (a millionth of a millionth of a watt). Negative dBm just means "less than 1 mW". Modern cellular UEs decode below −110 dBm thanks to forward error correction and processing gain.

Is +3 dBm really "double the power" of 0 dBm?

Yes, almost exactly. 10^(3/10) = 1.995, so +3 dB = 1.995×. 0 dBm = 1 mW, so +3 dBm = ~2 mW. The "3 dB = double power" rule comes from the fact that log₁₀(2) ≈ 0.301, and 10 · 0.301 = 3.01. Engineers round to 3 for convenience.

How does V_rms change with impedance?

Voltage for a given power depends on the load: V = √(P × R). So 1 W into 50 Ω = ~7.07 V, but 1 W into 600 Ω = ~24.5 V, and 1 W into 75 Ω = ~8.66 V. RF: usually 50 Ω. Antenna/cable systems: 75 Ω. Pro audio (legacy): 600 Ω. Modern audio: ~10 kΩ (high-impedance bridging). This tool shows the 50 Ω value because that's the most common RF reference.

Why doesn't this tool accept negative power?

Power is the product of voltage and current. A negative number for power would imply energy flowing the other way (e.g., into a source), which doesn't apply to RF/audio signal levels. If you're measuring instantaneous power that swings positive and negative (rare), take the time-average or RMS first. The dB scale is only defined for positive ratios.

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