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Math Engine

Decibel Calculator

Professional logarithmic operations for RF power summation, subtraction, and linear conversions.

power addition

combining power from multiple sources (incoherent addition). result = 10 × log₁₀(Σ 10^(dbi/10))

incoherent summation
dbm/dbi

primary signal power level

dbm/dbi

secondary signal power level

logarithmic scalars

standard power ratios (db ⇄ linear)

magnitude
ratio
description
-20 db
0.01
1% power
-10 db
0.1
10% power
-3 db
0.5
half power
0 db
1
unity base
+3 db
2
double power
+10 db
10
10x magnitude
+20 db
100
100x magnitude
+30 db
1000
1000x magnitude

summation cases

incoherent addition behaviors

delta
combined
log logic
30/30
33.0 db
equidistant (+3.0)
30/27
31.8 db
3db gap (+1.8)
30/24
31.0 db
6db gap (+1.0)
30/20
30.4 db
10db gap (+0.4)
30/10
30.0 db
20db gap (~0.0)
40/37
41.8 db
shifted base (+1.8)
50/50
53.0 db
high base (+3.0)
engineering heuristic

signals with >20 db difference are mathematically negligible. the stronger signal defines the system output with <0.1 db error.

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