A decibel (dB) is a logarithmic unit expressing the ratio between two signal levels. For voltage: dB = 20 log₁₀(V₂/V₁). For power: dB = 10 log₁₀(P₂/P₁). It compresses huge ranges into convenient numbers.

How do I cascade dB values?

Simply add them. A +20 dB amplifier followed by a −6 dB cable loss gives +14 dB total. This is much simpler than multiplying the equivalent linear ratios (10 × 0.5 = 5 = +14 dB).

0 dB means the ratio is 1:1 (no change). It does not mean zero signal. +3 dB doubles power, +6 dB doubles voltage, +10 dB is 10× power, +20 dB is 10× voltage.

Why is the voltage formula 20 log instead of 10 log?

Because power is proportional to voltage squared (P = V²/R). So 10 log(V²) = 20 log(V). The factor of 2 accounts for the squared relationship. Both formulas give the same dB value for the same physical change.

Decibel Calculator

dB ↔ Voltage & Power Ratio — Enter Any One

dB Decibels

Enter dB to find ratios

V Voltage Ratio (V₂/V₁)

Enter ratio to find dB

P Power Ratio (P₂/P₁)

Enter ratio to find dB

Enter dB, voltage ratio, or power ratio

Decibel Conversion

Decibels
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dB

Voltage Ratio

—

Power Ratio

—

Visual Comparison (linear scale, normalised to 0 dB = 100%)

Reference

0 dB

Voltage

—

Power

—

Voltage Change

—

Power Change

—

Nepers

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Figure 1: The decibel scale compresses huge ranges. +3 dB doubles power, +6 dB doubles voltage, +20 dB is 10× voltage (100× power). For absolute levels, dBm references 1 mW.

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Table of Contents

Fundamentals

What Is a Decibel?
The Formulas
Common dB Values

Mode Guides

Mode 1 — dB ↔ Ratio
Mode 2 — dBm ↔ Watts
Mode 3 — Cascade Stages

Deep Dive

dB vs dBm — The Key Difference
Why 20 × log for Voltage?
What Does 0 dB Mean?
Nepers

Reference

Frequently Asked Questions
Related Calculators

What Is a Decibel?

A decibel (dB) is a logarithmic ratio between two quantities. It compresses huge ranges into manageable numbers: a million-to-one power ratio is just 60 dB, and a thousand-to-one voltage ratio is also 60 dB. The logarithmic scale matches how we perceive sound and how signal chains accumulate gain and loss — dB values simply add, while linear ratios multiply.

The calculator above has three modes. Mode 1 converts between dB and voltage/power ratios in both directions. Mode 2 converts between dBm and watts with V_rms at 50 Ω and 600 Ω. Mode 3 cascades up to 8 gain/loss stages for link budgets. The Gain Calculator uses the same dB principles for amplifier analysis.

The Formulas

Voltage/amplitude: dB = 20 × log₁₀(V_out/V_in)
Power: dB = 10 × log₁₀(P_out/P_in)
Reverse: Voltage ratio = 10^(dB/20) | Power ratio = 10^(dB/10)
Nepers: Np = dB / 8.686

The factor is 20 for voltage because power is proportional to voltage squared (P ∝ V²). When you square a ratio then take the log, you get an extra factor of 2. So 20 × log(V) and 10 × log(P) always give the same dB value for the same physical change.

Common dB Values

dB	Voltage Ratio	Power Ratio	Meaning
+60	1000×	1,000,000×	High-gain amplifier
+40	100×	10,000×	Strong amplification
+20	10×	100×	Moderate gain
+10	3.162×	10×	Ten times the power
+6	2.0×	3.98×	Voltage doubles
+3	1.414×	2.0×	Power doubles
0	1.0×	1.0×	No change
−3	0.707×	0.5×	Power halves (−3 dB point)
−6	0.5×	0.25×	Voltage halves
−10	0.316×	0.1×	10 dB attenuation
−20	0.1×	0.01×	20 dB loss

Mode 1 — dB ↔ Ratio

Enter any one of dB, voltage ratio, or power ratio. The calculator returns all three plus voltage percentage change, power percentage change, and the equivalent in nepers. A visual bar comparison shows input versus output relative to the 0 dB reference.

Example: +20 dB

Given: +20 dB

Voltage ratio = 10^(20/20) = 10×

Power ratio = 10^(20/10) = 100×

Voltage change: +900% | Power change: +9,900%

Nepers: 20 / 8.686 = 2.303 Np

Example: Enter Voltage Ratio 0.5× → Find dB

Given: Voltage ratio = 0.5

dB = 20 × log₁₀(0.5) = 20 × (−0.301) = −6.02 dB

Power ratio = 0.5² = 0.25× (−6 dB power)

Voltage drops by 50%, power drops by 75%.

The Signal Attenuation Calculator applies these dB ratios to real cable runs, showing how signal weakens over distance and through connectors.

Mode 2 — dBm ↔ Watts

dBm is an absolute power level referenced to 1 milliwatt. 0 dBm = 1 mW. Enter dBm or watts — the calculator converts both ways and shows dBm, watts, milliwatts, dBW, and V_rms at both 50 Ω (RF standard) and 600 Ω (audio standard).

dBm to watts: P (mW) = 10^(dBm/10)
Watts to dBm: dBm = 10 × log₁₀(P_mW)
dBW: dBW = dBm − 30
V_rms: V = √(P × R) — voltage across a given impedance

Common dBm Values

dBm	Power	V_rms (50Ω)	Typical Use
−30	1 µW	0.224 mV	Very weak received signal
−10	100 µW	2.24 mV	Typical receiver input
0	1 mW	224 mV	Reference level
+10	10 mW	707 mV	Low-power transmitter
+20	100 mW	2.24 V	Wi-Fi access point
+30	1 W	7.07 V	Handheld radio
+37	5 W	15.8 V	Mobile base station
+47	50 W	50 V	VHF/UHF repeater

Example: 20 dBm

Given: 20 dBm

P = 10^(20/10) = 100 mW = 0.1 W

dBW = 20 − 30 = −10 dBW

V_rms (50Ω) = √(0.1 × 50) = √5 = 2.236 V

V_rms (600Ω) = √(0.1 × 600) = √60 = 7.746 V

Example: Enter 5 W → Find dBm

Given: 5 watts

dBm = 10 × log₁₀(5000) = 36.99 ≈ 37 dBm

dBW = 10 × log₁₀(5) = 6.99 ≈ 7 dBW

V_rms (50Ω) = √(5 × 50) = √250 = 15.81 V

Mode 3 — Cascade Stages

Build a signal chain with up to 8 stages. Each stage has a positive (gain) or negative (loss) dB value. The calculator shows a running total at each stage plus the final totals: total dB, total voltage ratio, and total power ratio.

Key principle: dB values add. Linear ratios multiply. A +20 dB amplifier followed by a −6 dB cable followed by a +10 dB amplifier: 20 + (−6) + 10 = +24 dB total. In linear terms: 10 × 0.5 × 3.162 = 15.81× voltage ratio. Same answer, but the dB arithmetic is far simpler.

Example: Amplifier → Cable → Amplifier

3-stage cascade

Stage 1: +20 dB (preamp) → running total: +20 dB

Stage 2: −3 dB (cable loss) → running total: +17 dB

Stage 3: +10 dB (power amp) → running total: +27 dB

Voltage ratio = 10^(27/20) = 22.39×

Power ratio = 10^(27/10) = 501.2×

Example: RF Receiver Chain

6-stage receiver link budget

Stage 1: Antenna gain +3 dBi → +3 dB

Stage 2: Coax loss −2 dB → +1 dB

Stage 3: Band-pass filter −1.5 dB → −0.5 dB

Stage 4: LNA +25 dB → +24.5 dB

Stage 5: Mixer conversion loss −7 dB → +17.5 dB

Stage 6: IF amplifier +30 dB → +47.5 dB

Power ratio = 56,234×

This is a link budget — the foundation of every RF system design. Each component’s gain or loss is listed, and the running total tells you whether the signal arrives at the demodulator above the minimum sensitivity threshold. The Noise Figure Calculator extends this by analysing how noise accumulates through the same chain using the Friis formula.

dB vs dBm — The Key Difference

dB is a relative ratio. It compares two values: output to input. +6 dB means the output is twice the input voltage. It does not tell you the absolute level — just how much bigger or smaller one is relative to the other.

dBm is an absolute level. It compares power to a fixed reference: 1 mW. 0 dBm = 1 mW, always. +20 dBm = 100 mW, always. You can convert dBm to watts and back because the reference point is defined.

You can add dB to dBm: a +20 dBm signal through a +10 dB amplifier becomes +30 dBm. But you cannot add dBm to dBm — that is adding two absolute levels, which does not make physical sense.

Why 20 × log for Voltage but 10 × log for Power?

Power is proportional to voltage squared (P = V²/R). Taking the log of V² gives 2 × log(V). So 10 × log(P) = 10 × log(V²/R) = 20 × log(V) − 10 × log(R). When comparing ratios at the same impedance, the R terms cancel and you are left with 20 × log(V_ratio) for voltage and 10 × log(P_ratio) for power. Both give the same dB number for the same physical change — they are not different scales, just different entry points into the same scale.

What Does 0 dB Mean?

0 dB means no change — the ratio is 1:1, output equals input. It does not mean silence, zero power, or off. A 0 dB gain stage passes the signal through unchanged. A 0 dBm signal has 1 mW of power — it is the reference level, not zero. The Bandwidth Calculator uses the −3 dB point (half-power point) as the standard cutoff frequency definition, which is 0.707× the peak voltage.

Nepers

The neper (Np) is the natural-logarithm equivalent of the decibel. 1 Np = 8.686 dB. Nepers appear in telecom standards, transmission line theory, and some European specifications. The calculator converts dB to nepers automatically in Mode 1.

Frequently Asked Questions

What is a decibel?

A logarithmic unit expressing the ratio between two values. 10 × log₁₀(power ratio) or 20 × log₁₀(voltage ratio). It compresses large ranges into small numbers and turns multiplication/division into addition/subtraction.

What is the difference between dB and dBm?

dB is a relative ratio (output vs input). dBm is an absolute power level referenced to 1 mW. You can add dB to dBm (+20 dBm + 10 dB = +30 dBm) but you cannot add dBm to dBm because that would be adding two absolute levels.

How do I cascade gain and loss stages?

Add the dB values. +20 dB gain + (−6 dB loss) + (+10 dB gain) = +24 dB total. This is equivalent to multiplying the linear ratios: 10 × 0.5 × 3.162 = 15.81×. The dB method is faster and less error-prone for long chains.

What does 0 dB mean?

Ratio of 1:1. No gain, no loss. Output equals input. It is not silence or zero power. 0 dBm specifically means 1 mW of power — that is the reference point, not zero.

Why is it 20 × log for voltage but 10 × log for power?

Because P ∝ V². The log of V² is 2 × log(V), so the voltage formula needs a factor of 20 (= 2 × 10) to produce the same dB number as the power formula’s factor of 10. Both give identical results for the same physical change.

How do I convert dBm to watts?

P (mW) = 10^(dBm/10). So 30 dBm = 10³ = 1000 mW = 1 W. The calculator also shows dBW (= dBm − 30) and V_rms at 50 Ω and 600 Ω.

What is a link budget?

A list of every gain and loss in a signal chain from transmitter to receiver, summed in dB. If the total received level exceeds the receiver’s minimum sensitivity, the link works. Mode 3 (Cascade Stages) builds this directly — enter each stage’s dB value and read the running total.

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Last updated: March 2026