About

Signal processing and electrical engineering rely heavily on logarithmic scales. This tool bridges the gap between logarithmic decibels and linear power units like Watts. Engineers use decibels because signal strengths vary over massive ranges. A linear scale becomes unreadable when comparing a picowatt signal to a megawatt transmission. The decibel compresses this range into manageable numbers.

Accuracy depends entirely on the reference level. A value in decibels is meaningless without knowing the zero point. This calculator handles the two most common standards. The first is dBW where the reference is one Watt. The second is dBm where the reference is one milliwatt. Users can also define arbitrary reference levels for specialized systems. Misinterpreting the reference unit leads to calculation errors by orders of magnitude.

Formulas

The conversion requires exponentiation of the base 10. The formula changes slightly depending on the reference power P₀.

P_watts = P₀ × 10^L_dB10

Where L_dB represents the level in decibels. For dBm conversions the reference P₀ is 0.001 Watts. For dBW the reference is 1 Watt.

Reference Data

Signal Level	Value (dBm)	Value (dBW)	Power (Linear)	Context
Thermal Noise	-174	-204	4 × 10^-21 W	GPS Noise Floor
Wi-Fi Rx	-80	-110	10 pW	Weak Signal
Bluetooth	0	-30	1 mW	Standard Class 2
Cell Phone	23	-7	200 mW	Max Transmission
Small Cell	30	0	1 W	Base Station
FM Radio	80	50	100 kW	Broadcast Tower
Radar Pulse	90	60	1 MW	Military Radar
Sound System	50	20	100 W	Concert Speaker

Frequently Asked Questions

Decibels define a ratio rather than an absolute quantity. Saying a signal is 10 dB just means it is ten times larger than something else. The reference level defines that something else. Without it the value implies nothing about physical energy.

These units measure the same physical property but start from different zero points. 0 dBW equals 1 Watt while 0 dBm equals 1 milliwatt. This means any value in dBW is exactly 30 units lower than the same power expressed in dBm.

Yes. Negative decibel values simply indicate that the power is less than the reference level. For example -10 dBW means the power is one-tenth of a Watt. This is common in receiver sensitivity and noise floor calculations.

A useful estimation trick involves the number 3. Increasing a signal by 3 dB approximately doubles its power. Decreasing it by 3 dB cuts the power in half. This works because 10 to the power of 0.3 is approximately 2.