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Decibel Calculator

Converts between a linear ratio and decibels using 10·log10 for power quantities or 20·log10 for amplitude quantities (voltage, current, sound pressure), and between dBm and milliwatts (0 dBm = 1 mW).

When to use

You need to express a gain, loss or signal ratio in dB, turn a dB figure back into a ratio, or convert an RF power level between dBm and mW/W.

Do not use when: You need to add two sound levels or account for distance attenuation, or you need plain logarithms (use logarithm).

Formula

power: dB = 10 × log10(ratio), ratio = 10^(dB/10); amplitude: dB = 20 × log10(ratio), ratio = 10^(dB/20); dBm = 10 × log10(P_mW), P_mW = 10^(dBm/10); dBW = dBm − 30

Amplitude quantities use 20·log10 because power is proportional to amplitude squared, so both conventions give the same dB for the same physical change. A negative dB value means attenuation (ratio below 1).

Inputs

Parameter	Type	Unit	Required	Description
`quantity`	enum: power \| amplitude \| dbm		default power	Whether the linear value is a power ratio, an amplitude (field) ratio, or an absolute power in mW for dBm.
`linear_value`	number		no	The ratio (output/input), or the power in milliwatts for quantity=dbm. Give either linear_value or decibel_value. Range: > 0
`decibel_value`	number	dB	no	Level in dB (or dBm for quantity=dbm). Give either linear_value or decibel_value.

Outputs

Output	Type	Unit	Description
`solved_for`	string		decibel_value or linear_value.
`decibel_value`	number	dB	10·log10(ratio) for power, 20·log10(ratio) for amplitude, 10·log10(mW) for dBm.
`linear_value`	number		The ratio, or milliwatts for dBm.
`power_ratio`	number		10^(dB/10): the power ratio corresponding to this dB value.
`amplitude_ratio`	number		10^(dB/20): the voltage/current ratio corresponding to this dB value (power and amplitude modes).
`milliwatts`	number	mW	Absolute power (dBm mode only).
`watts`	number	W	Absolute power in watts (dBm mode only).
`dbw`	number	dBW	dBm − 30 (dBm mode only).
`interpretation`	string		Plain-language reading of the result.

Example

Power ratio 1000: {"quantity":"power","linear_value":1000} → {"solved_for":"decibel_value","decibel_value":30,"power_ratio":1000,"amplitude_ratio":31.622777,"interpretation":"Gain of 30 dB: output power is 1000× the input"}

20 dBm to milliwatts: {"quantity":"dbm","decibel_value":20} → {"solved_for":"linear_value","linear_value":100,"milliwatts":100,"watts":0.1,"dbw":-10}

GET https://tttkmbb.com/api/v1/calculate/decibel?quantity=power&linear_value=1000

Machine access

API: GET https://tttkmbb.com/api/v1/calculate/decibel (query parameters) or POST with a JSON body {"inputs": {...}}
Schema: https://tttkmbb.com/api/v1/calculators/decibel · Markdown: https://tttkmbb.com/engineering/decibel.md · JSON definition: https://tttkmbb.com/engineering/decibel.json
MCP: server https://tttkmbb.com/mcp, tool run_calculator with calculator_id="decibel"
OpenAPI operationId: convert_decibels
Freshness: static. Authentication: none. Rate limit: fair use (see rate limits).

Sources

Wikipedia – Decibel (reference)
Wikipedia – dBm (reference)
NIST Special Publication 811 – Guide for the Use of the SI, Appendix B (conversion factors) (standard)

FAQ

Is doubling 3 dB or 6 dB?

Doubling the power is +3.01 dB; doubling the voltage (or current or sound pressure) is +6.02 dB, which is also a 4× power increase.

What is the difference between dB and dBm?

dB is a ratio with no unit; dBm is an absolute power referenced to 1 mW (0 dBm = 1 mW, 30 dBm = 1 W, −30 dBm = 1 µW).

Related calculators

Logarithm Calculator — The underlying base-10 logarithm.
Electric Power Calculator — Absolute electrical power from voltage and current.
Exponent Calculator — Evaluate 10^(dB/10) directly.