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Power Conversion Calculator

Our free electrical & magnetic converter handles power conversion conversions. See tables, ratios, and examples for quick reference.

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Unit Conversion

Power Conversion Calculator

Convert power between watts, kilowatts, horsepower, BTU/h, calories per second, dBm, and more with instant results.

Last updated: December 2025

Calculator

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Conversion Result
1 Watt (W) 1.000000e-3 Kilowatt (kW)

All Conversions from 1.0000 W

UnitValue
Watt (W)1.000000e+0
Kilowatt (kW)1.000000e-3
Megawatt (MW)1.000000e-6
Gigawatt (GW)1.000000e-9
Milliwatt (mW)1.000000e+3
Microwatt (uW)1.000000e+6
Horsepower (mechanical)1.341022e-3
Horsepower (electrical)1.340483e-3
Horsepower (metric)1.359622e-3
BTU per hour (BTU/h)3.412142e+0
Calorie per second (cal/s)2.388459e-1
Foot-pound per second (ft*lbf/s)7.375621e-1
Volt-ampere (VA)1.000000e+0
dBm (relative to 1 mW)30.00 dBm
Your Result
1 Watt (W) = 1.000000e-3 Kilowatt (kW)
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Understand the Math

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.

Last reviewed: December 2025

Worked Examples

Example 1: Motor Power Rating

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

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
Expert Insights

Background & Theory

The Power Conversion Calculator applies the following established principles and formulas. Unit conversion is the process of expressing a quantity in a different unit of measurement while preserving its physical meaning. At the foundation of modern measurement lies the International System of Units (SI), which defines seven base units: the meter for length, kilogram for mass, second for time, ampere for electric current, kelvin for thermodynamic temperature, mole for amount of substance, and candela for luminous intensity. All other units, called derived units, are defined as algebraic combinations of these seven. Dimensional analysis is the principal method for performing unit conversions. By treating units as algebraic quantities that can be multiplied, divided, and cancelled, a conversion factor chain allows a value expressed in one unit to be rewritten in another without altering its physical magnitude. For example, to convert 60 miles per hour to meters per second, one multiplies by a chain of conversion factors each equal to one: (1609.34 m / 1 mile) ร— (1 hour / 3600 s). Metric prefixes enable compact expression of quantities across extreme ranges of magnitude. Standard prefixes span from nano (10^-9) through micro (10^-6) and milli (10^-3) up through kilo (10^3), mega (10^6), and giga (10^9), and beyond in both directions. These prefixes are strictly multiplicative and apply consistently to any SI base or derived unit. Temperature conversions require affine transformations rather than simple scaling. To convert Celsius to Fahrenheit the formula is ยฐF = (ยฐC ร— 9/5) + 32, while the conversion to the absolute Kelvin scale is K = ยฐC + 273.15. These formulas reflect the different zero points and degree-size conventions of each scale. Significant figures govern how precision is preserved through calculations. A result should not express more precision than the least precise input value permits. In digital storage, IEEE and IEC standards distinguish between decimal prefixes (kilobyte = 1000 bytes) and binary prefixes (kibibyte = 1024 bytes), a distinction that has practical consequences for how storage capacity is reported by manufacturers versus operating systems. Unit coherence โ€” ensuring that all quantities in an equation share a consistent unit system โ€” is essential for obtaining correct results.

History

The history behind the Power Conversion Calculator traces back through the following developments. Human beings have been measuring and comparing quantities since before recorded history. The earliest known measurement units were body-based: the cubit (the distance from elbow to fingertip), the foot, the hand, and the digit. The furlong originated as the length of a furrow a team of oxen could plow without resting. These anthropomorphic standards were practical for local use but differed between regions and kingdoms, creating persistent difficulties in trade and construction. The ancient Egyptians standardized the royal cubit at approximately 52.4 centimeters and distributed calibrated granite rods to ensure consistency across building projects, including the pyramids. Roman engineers used the mile (mille passuum, one thousand double paces) and spread these standards throughout their empire via road networks. Despite these efforts, measurement diversity persisted across medieval Europe, hampering commerce. The French Revolution created political will for radical standardization. In 1795 France officially adopted the metric system, defining the meter as one ten-millionth of the distance from the equator to the North Pole along the Paris meridian. This gave the world its first fully decimal, rationally constructed measurement system. The Metre Convention of 1875 established the International Bureau of Weights and Measures (BIPM) in Sevres, France, creating a permanent international body to maintain physical artifact standards and coordinate global metrology. For over a century, the kilogram was defined by a platinum-iridium cylinder locked in a vault near Paris. In 1999, a stark demonstration of what unit inconsistency costs occurred when NASA's Mars Climate Orbiter was lost because one engineering team used pound-force seconds while another used newton seconds. The spacecraft entered the Martian atmosphere at the wrong angle and was destroyed, at a cost of 327 million dollars. In 2019 the SI underwent its most significant revision, redefining all seven base units in terms of fixed numerical values of fundamental physical constants such as the speed of light, Planck's constant, and the elementary charge. This eliminated any reliance on physical artifacts and made the measurement system permanently stable and universally reproducible.

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Frequently Asked Questions

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.
Common errors include confusing fluid ounces with weight ounces, mixing up miles and nautical miles, forgetting that UK and US gallons differ (UK is 20% larger), using the wrong temperature formula, and not accounting for the difference between troy and avoirdupois ounces.
You may use the results for reference and educational purposes. For professional reports, academic papers, or critical decisions, we recommend verifying outputs against peer-reviewed sources or consulting a qualified expert in the relevant field.
All calculations use established mathematical formulas and are performed with high-precision arithmetic. Results are accurate to the precision shown. For critical decisions in finance, medicine, or engineering, always verify results with a qualified professional.
No. All calculations run entirely in your browser using JavaScript. No data you enter is ever transmitted to any server or stored anywhere. Your inputs remain completely private.
The Formula section on this page shows the equation used. You can reproduce the calculation manually or in a spreadsheet using those steps. Compare your answer against the worked examples in the Examples section, which use known reference values so you can confirm the calculator is behaving as expected.
Educational Note: This calculator is provided for educational and informational purposes. Results are based on the formulas and inputs provided. Always verify important calculations independently. NovaCalculator processes calculator inputs client-side; optional analytics follow visitor consent settings. ยฉ 2024โ€“2026 NovaCalculator.

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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\nKilowatts = 3728.5 / 1000 = 3.7285 kW\nBTU/h = 3728.5 x 3.41214 = 12,723 BTU/h\nThis 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\nP_W = 100 / 1000 = 0.1 W\n20 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 are the most common unit conversion mistakes?

Common errors include confusing fluid ounces with weight ounces, mixing up miles and nautical miles, forgetting that UK and US gallons differ (UK is 20% larger), using the wrong temperature formula, and not accounting for the difference between troy and avoirdupois ounces.

Can I use Power Conversion Calculator on a mobile device?

Yes. All calculators on NovaCalculator are fully responsive and work on smartphones, tablets, and desktops. The layout adapts automatically to your screen size.

Why might my result differ from another tool or reference?

Differences typically arise from rounding conventions, the specific version of a formula (for example, simple vs compound interest), or unit inconsistencies between inputs. Check that both tools are using the same formula variant and the same units. The References section links to the authoritative source behind the formula used here.

How accurate are the results from Power Conversion Calculator?

All calculations use established mathematical formulas and are performed with high-precision arithmetic. Results are accurate to the precision shown. For critical decisions in finance, medicine, or engineering, always verify results with a qualified professional.

Is my data stored or sent to a server?

No. All calculations run entirely in your browser using JavaScript. No data you enter is ever transmitted to any server or stored anywhere. Your inputs remain completely private.

References

Reviewed by Manoj Kumar, Mathematics Educator ยท Editorial policy