Convert power ratio to dB

Convert a power ratio (P1 / P2) into decibels (dB).

Numerator

Denominator

Decibels

—dB

History

Press Enter in any field to keep a snapshot here.

Formula

Formula: dB = 10 × log₁₀(P1 / P2)
Note the factor of 10 for power (voltage uses 20)

Design notes

Power ratios use a different factor from voltage ratios (10×log against 20×log). RF design deals in power most of the time, so this is the version you reach for.

Why the factor differs: since P = V²/R, power goes with the square of voltage. Squaring doubles the logarithm, so the multiplier is halved (20 → 10).

When you need this

For expressing a ratio of two powers in dB. Transmit power, cable loss, antenna gain and isolation are all power-referenced, which is the standard basis in RF work.

Power ratios use 10·log₁₀

dB = 10 × log₁₀(P1 / P2). The factor differs from the 20 used for voltage, so mixing them up gives a two-fold error.

In RF, impedances are standardised at 50Ω, which makes working in power natural. Transmit power (dBm), cable loss (dB/m) and antenna gain (dBi) are all power-based.

Using it for a link budget

The convenience of dB is that multiplication becomes addition. Write every element of the path in dB and simply add and subtract to get the received power.

A 920MHz LPWA example.
Item	Value	Running total
Transmit power	+13 dBm	13 dBm
Transmit cable loss	−1 dB	12 dBm
Transmit antenna gain	+2 dBi	14 dBm
Free-space loss (1km)	−92 dB	−78 dBm
Receive antenna gain	+2 dBi	−76 dBm
Receive cable loss	−1 dB	−77 dBm

Against a module sensitivity of −120dBm, the link margin is 43dB. Real deployments add fading from buildings and terrain, so budgeting 20–30dB of margin is normal.

Quick reference

3dB is twice, 10dB is ten times. For power, everything can be built from these two.
0dBm = 1mW, 30dBm = 1W. With these two anchors you can interpolate in 10dB steps.
Negative means loss. Cable loss, free-space loss and insertion loss are all negative dB.

Frequently asked questions

What is the difference between dBm and dB?

dB is a plain ratio (dimensionless); dBm is an absolute power referenced to 1mW. Subtracting dBm from dBm gives dB, and adding dB to dBm gives dBm. Mixing them up produces nonsensical units.

How do I calculate free-space loss?

FSPL[dB] = 20·log₁₀(d) + 20·log₁₀(f) + 32.44, with d in km and f in MHz. At 920MHz over 1km: 0 + 59.3 + 32.44 ≈ 91.7dB. Loss increases with both frequency and distance.

Any trick for not confusing this with the voltage form?

It comes down to remembering 10·log for power and 20·log for voltage, but keeping one concrete example handy helps: 3dB is twice in power but only 1.41 times in voltage. RF specifications are almost always power-based, while amplifier and filter specifications are usually voltage-based.

Standards and references

IEC 60027-3 — Definition of logarithmic quantities.
ITU-R P.525 — Calculation of free-space attenuation.

Last updated: 2026-08-29