1 watt (W) equals 30 decibels-milliwatts (dBm).
The conversion from watts to dBm involves using a logarithmic formula that translates power ratios into a decibel scale referenced to 1 milliwatt. Since 1 watt is 1000 milliwatts, the calculation converts this ratio into dBm scale, resulting in 30 dBm.
Conversion Tool
Result in dbm:
Conversion Formula
The formula to convert watts (W) to decibels-milliwatts (dBm) is:
dBm = 10 × log10(Power in milliwatts)
Since watts must be converted to milliwatts first, multiply by 1000:
dBm = 10 × log10(W × 1000)
This works because dBm is a logarithmic measure of power referenced to 1 milliwatt. Using the log scale compresses large power ranges into manageable numbers.
Example for 1 W:
- Convert 1 W to mW: 1 × 1000 = 1000 mW
- Calculate log base 10 of 1000: log10(1000) = 3
- Multiply by 10: 10 × 3 = 30 dBm
Conversion Example
- Convert 0.5 W to dBm:
- 0.5 W × 1000 = 500 mW
- log10(500) ≈ 2.69897
- 10 × 2.69897 = 26.9897 dBm
- Convert 2 W to dBm:
- 2 × 1000 = 2000 mW
- log10(2000) ≈ 3.30103
- 10 × 3.30103 = 33.0103 dBm
- Convert 0.1 W to dBm:
- 0.1 × 1000 = 100 mW
- log10(100) = 2
- 10 × 2 = 20 dBm
- Convert 5 W to dBm:
- 5 × 1000 = 5000 mW
- log10(5000) ≈ 3.69897
- 10 × 3.69897 = 36.9897 dBm
Conversion Chart
| Watts (W) | dBm |
|---|---|
| -24.0 | Invalid (negative power) |
| -20.0 | Invalid (negative power) |
| -10.0 | Invalid (negative power) |
| 0.0 | -∞ (0 watts means no power) |
| 1.0 | 30.0000 |
| 2.0 | 33.0103 |
| 5.0 | 36.9897 |
| 10.0 | 40.0000 |
| 15.0 | 41.7609 |
| 20.0 | 43.0103 |
| 25.0 | 43.9794 |
| 26.0 | 44.1461 |
The chart shows watts in the left column and corresponding dBm values on the right. Negative watt values are invalid for conversion because power can’t be negative. Zero watts corresponds to no power, which is negative infinity in dBm scale. Use the chart to quickly estimate dBm from known watt values.
Related Conversion Questions
- How many dBm is 1 watt equal to?
- What formula converts 1 watt to dBm?
- Is 1 watt equal to 30 dBm in power units?
- How to calculate dBm from 1 watt value?
- Why does 1 watt correspond to 30 dBm?
- What is the dBm equivalent of 1 watt in radio systems?
- Can you convert 1 watt to dBm without a calculator?
Conversion Definitions
W (watt): Watt is a unit of power measuring the rate of energy transfer or conversion. It equals one joule per second. In electrical contexts, watt quantifies the real power consumed or produced by a device. It is a standard SI unit used in many fields including electronics, mechanics, and lighting.
dBm: dBm is a power measurement unit expressed in decibels relative to one milliwatt (mW). It’s a logarithmic unit that indicates the ratio of a power level to 1 mW, often used in radio, audio, and telecommunications to quantify power levels in a manageable scale.
Conversion FAQs
Can the watt to dBm conversion handle values less than 1 watt?
Yes, the formula works for values less than 1 watt. Since it’s logarithmic, values below 1 watt will produce negative dBm values, indicating power levels below 1 milliwatt. For example, 0.001 W equals 0 dBm because 0.001×1000=1 mW.
What happens if I input zero or negative watts in the conversion?
Zero watts means no power, so the logarithm is undefined and the dBm value tends to negative infinity. Negative power values are physically invalid and the logarithm cannot be calculated. Conversion tools will usually show errors or empty results for such inputs.
Why use dBm instead of watts in radio frequency measurements?
dBm compresses a wide range of power values into a smaller scale making it easier to compare and calculate gains or losses. It also directly relates to the reference power of 1 milliwatt, which is convenient in RF engineering and signal strength representation.
Is the conversion from watts to dBm reversible?
Yes, you can convert dBm back to watts by reversing the formula: Watts = 10^(dBm/10) / 1000. This allows switching between logarithmic and linear power units whenever needed for calculations or measurements.
Can this conversion be used for both AC and DC power?
The conversion applies to power measured in watts regardless of AC or DC. However, in AC circuits, power factors and RMS values affect the actual power, so the watt value should be the real power before converting to dBm for accurate interpretation.