Mathematics & Conversions

dB to Linear Converter — Decibel, Power & Amplitude Ratio Calculator

Convert dB to linear ratios or referenced values and back using power (10·log₁₀) or amplitude/field (20·log₁₀) relationships, with additional log₁₀ and natural-log conversions.

Unit-aware inputs Deterministic calculation Engineering interpretation
Calculation workspace

Enter the known values and review the calculated result

Deterministic calculation
01
Parameters

Input parameters

Use consistent values and select the intended engineering units.

Conversion settings

Linear ratio

Decibel value

Value

Reference value

Linear value

Logarithmic value

02
Output

Results

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Engineering reference

Method, application and limitations

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01
Method

Formula and calculation method

Decibel and linear-ratio conversion:

L = n · log10(R)

R = 10L / n

where the decibel factor is:

  • n = 10 for power or energy quantities
  • n = 20 for amplitude or field quantities

For Linear ratio → dB, the entered ratio R is converted directly:

L = n · log10(R)

For dB → Linear ratio:

R = 10L / n

For Value / reference → dB:

R = X / Xref

L = n · log10(X / Xref)

For dB + reference → Value:

R = 10L / n

X = Xref · R = Xref · 10L / n

Base-10 logarithm conversions:

y = log10(X)

X = 10y

Natural logarithm conversions:

y = ln(X)

X = ey

where:

  • L — decibel value [dB]
  • R — positive linear ratio [–]
  • X — value being compared with a reference, or positive dimensionless value for log10 and ln conversion
  • Xref — positive reference value in the same unit as X
  • n — decibel conversion factor, equal to 10 for power/energy or 20 for amplitude/field quantities [–]
  • y — logarithmic value [–]

The 20·log10 relationship is appropriate for amplitude or field quantities when the corresponding power ratio is proportional to the square of the amplitude ratio under compatible reference conditions.

02
Application

When to use this calculator

Use this calculator to convert between logarithmic and linear representations when the applicable power or amplitude relationship is known.

  • Convert a positive linear power or energy ratio to decibels using 10 · log10(R).
  • Convert a positive amplitude or field ratio to decibels using 20 · log10(R).
  • Convert a dB value back to its corresponding linear power or amplitude ratio.
  • Convert an actual value relative to a positive reference value into dB.
  • Recover an actual value from a dB level and a specified reference value.
  • Convert an SNR expressed in dB to a linear signal-to-noise power ratio.
  • Convert positive dimensionless values to log10 or ln and perform the corresponding inverse exponential conversion.

When this calculator is not sufficient

The calculator does not automatically define reference levels for quantities such as dBm, dBW, dBV, dBu or dB SPL, perform unit conversions, or account for impedance, frequency weighting, bandwidth, measurement uncertainty or other application-specific corrections. If a named decibel level is being used, the correct reference value and quantity convention must be established separately.

03
Decision support

How to interpret the result

A decibel result represents a logarithmic ratio. A linear result represents either the ratio corresponding to the entered dB value or an actual value reconstructed from that ratio and the entered reference.

Interpreting dB and linear ratios

  • R = 1 corresponds to 0 dB.
  • R > 1 produces a positive dB value.
  • 0 < R < 1 produces a negative dB value.
  • For a power quantity, +10 dB corresponds to a linear power ratio of 10.
  • For an amplitude quantity, +20 dB corresponds to a linear amplitude ratio of 10.

The same numerical dB value therefore produces different linear ratios depending on whether Power / energy quantity or Amplitude / field quantity is selected.

Referenced values

In Value / reference → dB mode, the calculator first forms the dimensionless ratio X/Xref. A result of 0 dB means X equals Xref. A positive result means X is above the reference, while a negative result means X is below the reference.

In dB + reference → Value mode, the calculated linear ratio is multiplied by Xref. The resulting value therefore has the same unit as the reference value.

log10 and ln results

  • X = 1 gives log10(X) = 0 and ln(X) = 0.
  • X > 1 gives a positive logarithmic result.
  • 0 < X < 1 gives a negative logarithmic result.
  • The inverse log10 and ln modes return positive linear values through 10y and ey.

Result status

A valid calculation is returned with an Info interpretation status. Invalid is returned when a required value is missing or non-finite, a ratio or required reference is not greater than zero, the selected quantity type is invalid for a dB mode, or the inverse exponential result exceeds the numerical range of the calculator.

The status confirms only that the selected mathematical conversion was evaluated within the calculator’s input and numerical-domain rules. It does not verify that the chosen dB convention or reference value is appropriate for a particular physical measurement.

04
Worked case

Calculation example

Example: convert a 20 dB signal-to-noise ratio to a linear power ratio.

Assume the reported SNR is defined from signal power divided by noise power.

  • Conversion mode: dB → Linear ratio
  • Quantity type: Power / energy quantity (10·log10)
  • L — decibel value: 20 dB

For a power ratio, n = 10.

R = 10L / n

R = 1020 / 10

R = 102 = 100

Result: the linear power ratio is 100.

An SNR of 20 dB therefore corresponds to a signal power that is 100 times the noise power when SNR is defined as a power ratio.

The quantity type is essential. If the same numerical value of 20 dB represented an amplitude or field ratio instead, the calculator would use 20·log10 and return 10 rather than 100.

This conversion does not determine whether the SNR is acceptable for a particular system; that requires application-specific performance criteria.

05
Model boundaries

Assumptions and limitations

  • Decibel calculations use base-10 logarithms.
  • Power and energy quantities use the factor 10 in the dB relationship.
  • Amplitude and field quantities use the factor 20 in the dB relationship.
  • A linear ratio entered for conversion to dB must be finite and greater than zero.
  • Values X and Xref used in a referenced dB conversion must both be finite and greater than zero.
  • X and Xref must use the same physical unit so that X/Xref is dimensionless.
  • The 20·log10 form assumes that the relevant power ratio is proportional to the square of the selected amplitude or field ratio. The calculator does not evaluate impedance or other conditions required to establish that relationship.
  • Linear inputs to log10(X) and ln(X) are treated as dimensionless and must be greater than zero.
  • dB and logarithmic inputs used for inverse conversion may be positive, zero or negative, provided they are finite and the resulting exponential value remains within the numerical range of the calculator.
  • A zero linear ratio is not converted to negative infinity; it is rejected as invalid by the calculator.
  • The calculator does not automatically apply reference definitions for dBm, dBW, dBV, dBu, dB SPL or other named logarithmic levels.
  • No unit conversion, impedance correction, frequency weighting, bandwidth correction, uncertainty analysis or measurement-system correction is included.
06
Questions

Frequently asked questions

How do you convert dB to a linear ratio?
For a power or energy quantity, use R = 10L/10. For an amplitude or field quantity, use R = 10L/20, where L is the value in dB. The correct relationship depends on the physical quantity represented by the decibel value.
How do you convert a linear ratio to dB?
For a positive power or energy ratio R, calculate L = 10 · log10(R). For a positive amplitude or field ratio, calculate L = 20 · log10(R). A ratio of 1 corresponds to 0 dB.
What is 20 dB as a linear value?
The answer depends on the quantity type. For a power ratio, 20 dB corresponds to 1020/10 = 100. For an amplitude or field ratio, 20 dB corresponds to 1020/20 = 10. Therefore, “20 dB to linear” does not have one unique answer unless the quantity type is specified.
Why does power use 10·log₁₀ while amplitude uses 20·log₁₀?
Power ratios are expressed directly as 10 · log10(P/Pref). When power is proportional to the square of an amplitude or field quantity, substituting that squared relationship introduces a factor of two, giving 20 · log10(A/Aref). The 20·log relationship should therefore be used only when the required physical relationship and reference conditions are appropriate.
How do I convert SNR from dB to a linear ratio?
When SNR is defined as signal power divided by noise power, use the power conversion R = 10SNR(dB)/10. For example, 20 dB corresponds to a linear signal-to-noise power ratio of 100. Select dB → Linear ratio and Power / energy quantity in the calculator.
What does 0 dB mean in linear terms?
Zero decibels corresponds to a linear ratio of 1 for both power and amplitude conversions because 100 = 1. In a referenced-value calculation, 0 dB means that the value X equals the reference value Xref.
Can I convert an actual value to dB relative to a reference value?
Yes. Select Value / reference → dB, enter X and Xref in the same unit, and select the appropriate quantity type. The calculator forms R = X/Xref and then applies either 10 · log10(R) for power/energy or 20 · log10(R) for amplitude/field quantities.
Is dB the same as dBm, dBW, dBV or dB SPL?
No. dB by itself expresses a logarithmic ratio, while named levels such as dBm, dBW, dBV and dB SPL use defined physical reference values. This calculator does not automatically select those reference definitions. The underlying conversion can be reproduced only when the appropriate reference value, units and power or amplitude convention are supplied correctly.
What is the difference between log₁₀ and ln?
log10(X) is the logarithm of X to base 10, while ln(X) is the natural logarithm to base e. Their inverse operations are 10y and ey, respectively. The calculator provides separate modes for both logarithms and their inverse conversions.
Can a linear ratio of zero be converted to dB?
No finite dB value is produced for a zero ratio because log10(0) is not finite. The calculator therefore requires linear ratios, referenced values and reference values used in forward logarithmic conversion to be greater than zero and returns an invalid result for zero or negative inputs.
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