Linear to dB Calculator

Calculator inputs

Conversion direction

Input method

Quantity type

Logarithmic formula

Automatic selects power or amplitude rules.

Reference preset

Decimal precision

Output or measured value

This value must be greater than zero.

Input or baseline value

The ratio equals output divided by input.

Custom reference value

Used only with the custom reference preset.

Decibel value

Positive values are gains. Negative values are losses.

Use unequal impedance correction

Available for voltage and current comparisons.

Input impedance

Output impedance

Cascaded gains

Separate multiple dB values with commas.

Cascaded losses

Loss values are subtracted from total gain.

Formula used

Power ratios use ten times the base-ten logarithm. Amplitude quantities normally use twenty times that logarithm. Equal impedance is required for simple voltage comparisons.

Power: dB = 10 × log₁₀(P₂ / P₁)
Amplitude: dB = 20 × log₁₀(A₂ / A₁)
Power ratio: P₂ / P₁ = 10^(dB / 10)
Amplitude ratio: A₂ / A₁ = 10^(dB / 20)

How to use

Select the required conversion direction.
Choose ratio or reference-based input.
Select the measured quantity type.
Enter positive linear values or any dB value.
Enable impedance correction when impedances differ.
Add cascaded gains and losses when needed.
Choose precision, then calculate the result.
Copy, print, or export the completed calculation.

Common conversion examples

Application	Linear ratio	Formula	Result
Power doubles	2	10 × log₁₀(2)	3.0103 dB
Voltage doubles	2	20 × log₁₀(2)	6.0206 dB
Power becomes one tenth	0.1	10 × log₁₀(0.1)	−10 dB
Amplitude becomes one half	0.5	20 × log₁₀(0.5)	−6.0206 dB

Practical applications

Audio engineers compare signal levels and equipment gain. RF designers evaluate link budgets and component losses. Electronics work uses decibels for wide measurement ranges.

Frequently asked questions

1. What is a linear ratio?

A linear ratio directly compares two positive quantities. A ratio of two means the output doubled. Ratios below one represent a reduction.

2. Why are power ratios multiplied by ten?

Decibels were originally defined using power relationships. The logarithmic power definition uses a factor of ten. This preserves standard engineering conventions.

3. Why are voltage ratios multiplied by twenty?

Power is proportional to voltage squared at equal impedance. Logarithms convert that square into a factor of two. Ten therefore becomes twenty.

4. Can a dB value be negative?

Yes, negative decibels indicate a ratio below unity. They usually describe attenuation or signal loss. Zero decibels means no relative change.

5. Can zero be converted to decibels?

No finite decibel value represents a zero linear ratio. Its logarithm approaches negative infinity. The calculator therefore rejects zero inputs.

6. What does dBm measure?

dBm expresses power relative to one milliwatt. Zero dBm equals exactly one milliwatt. Positive values represent more power.

7. What does dBV measure?

dBV expresses voltage relative to one volt. Zero dBV equals exactly one volt. It is common in audio measurements.

8. When should impedance correction be enabled?

Enable correction when compared voltage or current impedances differ. The calculator then evaluates their true power ratio. This avoids misleading amplitude-only results.

9. How are cascaded gains combined?

Individual decibel gains are added together. Listed losses are subtracted from that total. This simplifies multi-stage system calculations.