Elara Bennett1 watt (W) is equal to 30 decibels-milliwatts (dBm).
The conversion from watts to dBm uses a logarithmic scale to express power levels relative to 1 milliwatt (mW). Since 1 W equals 1000 mW, the formula calculates how many decibels above 1 mW the power is, 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(W × 1000)
This formula works because dBm measures power relative to 1 milliwatt (mW). Since 1 watt is 1000 milliwatts, multiplying by 1000 converts watts to milliwatts. Applying the logarithm expresses the power on a logarithmic scale, reflecting how power levels are commonly compared in electronics and communications.
Example calculation for 1 W:
- Convert 1 W to mW: 1 × 1000 = 1000 mW
- Take the base-10 logarithm: 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 W × 1000 = 2000 mW
- log10(2000) ≈ 3.30103
- 10 × 3.30103 ≈ 33.0103 dBm
- Convert 0.1 W to dBm
- 0.1 W × 1000 = 100 mW
- log10(100) = 2
- 10 × 2 = 20 dBm
- Convert 5 W to dBm
- 5 W × 1000 = 5000 mW
- log10(5000) ≈ 3.69897
- 10 × 3.69897 ≈ 36.9897 dBm
Conversion Chart
| Power (W) | Power (dBm) |
|---|---|
| 0.000001 | -60.0000 |
| 0.00001 | -50.0000 |
| 0.0001 | -40.0000 |
| 0.001 | -30.0000 |
| 0.01 | -20.0000 |
| 0.1 | -10.0000 |
| 1 | 0.0000 |
| 10 | 10.0000 |
| 100 | 20.0000 |
| 1000 | 30.0000 |
| 10000 | 40.0000 |
The chart shows power values in watts and their corresponding dBm. To use, find the watt value closest to your power, then read across to see the dBm equivalent. This helps to quickly estimate power levels without calculation.
Related Conversion Questions
- How many dBm is 1 watt equal to in radio systems?
- What is the dBm value for 1 W of power output?
- Can 1 watt be expressed in dBm, and how is it done?
- Why does 1 watt convert to 30 dBm?
- How to convert 1 watt to dBm manually?
- What formula should I use to change 1 W into dBm?
- Is 1 watt always 30 dBm in all power measurements?
Conversion Definitions
W (Watt): A watt is unit of power that measures the rate at which energy is transferred or converted. In electrical terms, one watt equals one joule of energy per second. It quantifies how much work is done or energy used, commonly used in electronics, lighting, and machinery to specify power consumption or output.
dBm (decibel-milliwatts): dBm is a logarithmic unit expressing power relative to 1 milliwatt (mW). It shows power levels on a scale where 0 dBm equals 1 mW. This unit is useful in communications and signal processing, providing a convenient way to compare power magnitudes that span many orders of magnitude.
Conversion FAQs
Why do we multiply watts by 1000 in the conversion formula?
Because dBm is referenced to milliwatts, converting watts to milliwatts is necessary. One watt equals 1000 milliwatts, and since the logarithm is taken relative to 1 mW, the power value must be in milliwatts. Without this, the dBm value would be incorrect.
Can dBm values be negative when converting from watts?
Yes, when the power in watts is less than 0.001 W (1 mW), the corresponding dBm value becomes negative. This means the power is below the 1 mW reference point, indicating a very low power level, common in sensitive signal measurements.
Is the conversion formula valid for any power value?
The formula applies to positive power values only. Zero or negative watt values are invalid in this context because logarithms of zero or negative numbers are undefined. Hence, the input must be a positive number to get a meaningful dBm result.
Why use a logarithmic scale like dBm instead of watts?
Power in many electronic systems spans a large range, from microwatts to kilowatts. Using dBm compresses this range into manageable numbers. Logarithms also make multiplication/division of power ratios simpler through addition/subtraction of dB values, which is practical for engineers and technicians.
Does the conversion formula change for AC or DC power?
The formula itself is the same for power measurement, regardless of AC or DC. However, care must be taken that the power quantity is the effective or average power in watts. Instantaneous power values or peak readings should not be directly converted without proper averaging.
