The conversion of 10 watts (W) to decibels-milliwats (dBm) is 40 dBm.
To convert watts to dBm, the formula used is 10 * log10(Power in W / 1mW). Since 1 watt equals 1000 milliwats, we first convert 10 W to milliwats (10,000 mW), then apply the logarithmic formula. Therefore, 10 W is 40 dBm because 10 * log10(10,000 / 1) equals 40.
Conversion Result
10 W equals 40 dBm, a measure often used in radio frequency power levels to express power relative to 1 milliwatt.
Conversion Tool
Result in dbm:
Conversion Formula
The formula to convert watts to dbm is: dbm = 10 * log10(W * 1000). Since 1 watt equals 1000 milliwats, multiplying watts by 1000 gives milliwats. The logarithm base 10 then quantifies how many times 10 must be multiplied to reach that power level. This works because decibels are logarithmic, comparing power levels to a reference point, 1 milliwatt. For example, for 10 W: 10 * log10(10 * 1000) = 10 * log10(10,000) = 10 * 4 = 40 dbm.
Conversion Example
- Convert 5 W to dbm:
- Step 1: Multiply 5 W by 1000 to get 5000 mW.
- Step 2: Calculate log10(5000) which is approximately 3.69897.
- Step 3: Multiply by 10: 10 * 3.69897 = 36.9897 dbm.
- Convert 2 W to dbm:
- Step 1: 2 W * 1000 = 2000 mW.
- Step 2: log10(2000) ≈ 3.3010.
- Step 3: 10 * 3.3010 = 33.0100 dbm.
- Convert 0.5 W to dbm:
- Step 1: 0.5 W * 1000 = 500 mW.
- Step 2: log10(500) ≈ 2.69897.
- Step 3: 10 * 2.69897 = 26.9897 dbm.
Conversion Chart
| Watts (W) | Power in dBm |
|---|---|
| -15.0 | -125.5232 |
| -10.0 | -120.0 |
| -5.0 | -114.9770 |
| 0.0 | -30.0 |
| 1.0 | 0.0 |
| 5.0 | 37.0 |
| 10.0 | 40.0 |
| 20.0 | 43.01 |
| 30.0 | 45.77 |
| 35.0 | 48.44 |
Use this chart to quickly find the dbm equivalent for given watt values by matching the wattage with the corresponding decibel-milliwatts.
Related Conversion Questions
- What is 10 W in dbm for RF power levels?
- How do I convert 10 watts to decibels-milliwats precisely?
- What is the dbm value for 10 W in wireless communication?
- Can I convert 10 W to dbm using an online calculator?
- What is the meaning of 40 dbm compared to 10 W?
- How many milliwats are in 10 W, and what is its dbm equivalent?
- Is 10 W considered high power in radio frequency terms?
Conversion Definitions
w
The symbol “w” stands for watt, a unit of power measuring the rate of energy transfer or conversion. It is used in electrical, mechanical, and thermal contexts, representing the amount of energy transferred per second, with 1 watt equaling 1 joule per second.
dbm
“dbm” signifies decibels relative to one milliwatt, expressing power levels logarithmically compared to 1 mW. It simplifies large or small power ratios into manageable numbers, with 0 dBm equaling 1 milliwatt, making it common in radio and audio applications.
Conversion FAQs
What does 40 dBm mean in terms of wattage?
40 dBm corresponds to 10 W, indicating a power level 10,000 times higher than 1 milliwatt, because 40 = 10 * log10(P / 1mW); reversing this gives P = 10^(40/10) mW = 10,000 mW or 10 W.
How is the conversion from watt to dbm affected by different power levels?
The conversion is logarithmic; doubling the wattage increases dbm by approximately 3 dB. For example, 1 W is 30 dBm, and 2 W is about 33 dBm. Small changes in wattage lead to noticeable shifts in dbm due to the logarithmic scale.
Why is dbm preferred over watts in radio communications?
dbm provides a more manageable scale for very high or low power levels, making it easier to compare and analyze signal strengths, especially across wide ranges, without dealing with large or tiny numbers.
