Power Conversion Calculator
Our free electrical & magnetic converter handles power conversion conversions. See tables, ratios, and examples for quick reference.
Power Conversion Calculator
Calculator
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Formula: Converted Value = Input x (From Factor / To Factor) | dBm = 10 x log10(P_mW)
Worked example โ 5 hp = 3728.5 W = 3.73 kW = 12,723 BTU/h
Formula
Converted Value = Input x (From Factor / To Factor) | dBm = 10 x log10(P_mW)
Power conversion uses the watt as the base SI unit. Linear units convert by multiplying by the source factor and dividing by the target factor. The dBm scale is logarithmic: dBm = 10 x log10(power in milliwatts). Each 3 dB increase doubles the power, and each 10 dB increase multiplies power by 10.
Worked Examples
Example 1: Motor Power Rating
Problem:A motor is rated at 5 mechanical horsepower. Convert to watts, kilowatts, and BTU/h.
Solution:Watts = 5 x 745.7 = 3728.5 W Kilowatts = 3728.5 / 1000 = 3.7285 kW BTU/h = 3728.5 x 3.41214 = 12,723 BTU/h This is a typical small industrial motor rating.
Result:5 hp = 3728.5 W = 3.73 kW = 12,723 BTU/h
Example 2: Wireless Signal Power
Problem:A Wi-Fi router transmits at 20 dBm. What is this in watts and milliwatts?
Solution:P_mW = 10^(20/10) = 10^2 = 100 mW P_W = 100 / 1000 = 0.1 W 20 dBm is the typical maximum allowed power for Wi-Fi in many countries.
Result:20 dBm = 100 mW = 0.1 W
Frequently Asked Questions
What is a watt and how does it relate to other power units?
A watt (W) is the SI unit of power, defined as one joule per second. It measures the rate of energy transfer or conversion. One watt equals the power produced when one ampere of current flows through one volt of potential difference (P = V x I). Common multiples include kilowatts (1 kW = 1000 W) for household appliances, megawatts for power plants, and milliwatts for electronic signals. The watt is named after Scottish inventor James Watt.
What is the difference between mechanical, electrical, and metric horsepower?
Mechanical (imperial) horsepower equals 745.7 watts and was defined by James Watt based on the power output of draft horses. Electrical horsepower is exactly 746 watts by convention, used for rating electric motors. Metric horsepower (PS or CV) equals 735.5 watts, defined as the power to lift 75 kilograms one meter per second. The differences are small but matter in precise engineering calculations and legal motor specifications.
How do I convert watts to BTU per hour?
To convert watts to BTU per hour, multiply by 3.41214. To convert BTU/h to watts, divide by 3.41214 (or multiply by 0.29307). For example, a 1500 W space heater produces about 5118 BTU/h. This conversion is essential in HVAC engineering where heating and cooling capacity is specified in BTU/h in the US but watts or kilowatts in most other countries. One ton of refrigeration equals 12,000 BTU/h or about 3517 W.
What is dBm and how does it relate to watts?
dBm is a logarithmic power unit referenced to one milliwatt (mW). The conversion formula is dBm = 10 x log10(P_mW), where P_mW is power in milliwatts. So 0 dBm equals 1 mW, 10 dBm equals 10 mW, 20 dBm equals 100 mW, and 30 dBm equals 1 watt. Negative dBm values represent sub-milliwatt powers. dBm is widely used in telecommunications, RF engineering, and fiber optics because it simplifies gain and loss calculations to addition and subtraction.
How do I combine gains and losses expressed in decibels?
Because the decibel scale is logarithmic, cascaded gains and losses add and subtract instead of multiplying. Starting at 30 dBm, which is 1 watt, a 3 dB loss leaves 27 dBm, or 500 milliwatts, since each 3 dB step halves or doubles the power and each 10 dB step divides or multiplies it by ten. Adding decibel figures along a signal chain is far quicker than repeatedly multiplying linear power ratios.
What is the difference between kilowatts and kilovolt-amperes?
Kilovolt-amperes measure apparent power, the product of RMS voltage and RMS current, while kilowatts measure real power, the part actually converted into work or heat. They are linked by the power factor: kW equals kVA multiplied by the power factor. At a power factor of 0.8, a 100 kVA supply delivers only 80 kW of real power. Generators and transformers are rated in kVA because their limits are set by current and voltage, not by the load's phase angle.
How do I convert watts into calories per second or kilocalories per hour?
One thermochemical calorie is defined as 4.184 joules, so one watt equals 1/4.184 = 0.2390 calories per second. Multiplying by 3600 seconds and dividing by 1000 gives 0.8604 kilocalories per hour per watt. These conversions appear in heat transfer work and on exercise equipment, where the dietary Calorie with a capital C is in fact a kilocalorie, a factor of 1000 trap worth checking before converting.
How does a ton of refrigeration relate to watts?
One ton of refrigeration is defined as 12,000 BTU per hour, a rate historically tied to melting a short ton of ice in a day. Since one BTU per hour is about 0.29307 watts, a ton of refrigeration equals roughly 3,516.9 watts, or 3.517 kilowatts of heat removal. Chiller and air conditioning capacities are commonly quoted in tons in North America and in kilowatts elsewhere, so this factor bridges the two catalogues.
How does mechanical power relate to torque and rotational speed?
Mechanical power is torque multiplied by angular velocity. In SI units, power in watts equals torque in newton-metres times speed in radians per second, which is 2 pi times revolutions per second. In customary units the shortcut is horsepower equals torque in pound-feet times RPM divided by 5252, where 5252 is simply 33,000 divided by 2 pi. That constant is why a torque curve and a horsepower curve always cross at 5252 RPM.
What is the difference between RMS power and peak power in audio ratings?
RMS power is the continuous average power an amplifier or speaker can sustain, derived from RMS voltage and current, and it is the figure that predicts real thermal loading. Peak or music power describes brief transients and is usually quoted as a much larger number with no consistent measurement standard behind it. When converting an audio rating into watts for a power budget, use the continuous RMS figure and treat peak claims as marketing.
References
Reviewed for accuracy by Manoj Kumar, Mathematics Educator ยท Editorial policy
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