Toolarithm

Unit Converter

Energy Converter

Exact energy. Clear power-time models.

Convert an energy quantity

Exact conventions. Clear power-time models.

Signed decimal, scientific notation, fraction or mixed number. Negative energy denotes a declared change or transfer direction.

Optional energy-charge estimate

Energy-charge arithmetic excludes fixed fees, taxes, tiered prices, exchange rates and equipment losses. A negative result is a signed difference, not a promised credit.

View energy results
Precision and report

Decimals support twenty significant digits, eighty characters and written exponents from negative thirty through thirty. Fractions support one hundred digits per component and two hundred forty characters per field. Display precision does not improve measured power, energy or a tariff assumption.

Worked examples

Energy in joules

Et=3600000.00000 JE_t=3600000.00000\,\mathrm J

Exact named unit factors and numerical arithmetic; only displayed values are rounded. Signed values follow your declared energy-change or transfer direction.

Energy conversion record

Entered energy

Es=1.00000000000 kW hE_s=1.00000000000\,\mathrm{kW\,h}

Normalized energy

EJ=3600000.00000 JE_{\mathrm J}=3600000.00000\,\mathrm J

Energy in kilowatt-hours

EkW h=1.00000000000 kW hE_{\mathrm{kW\,h}}=1.00000000000\,\mathrm{kW\,h}

Source-to-target factor

k=3600000.00000k=3600000.00000

Energy and power are different quantities. A watt-hour includes elapsed time; a watt alone does not. Foot-pound-force here describes work through distance, while a torque value needs its own rotational context.

Energy in every supported convention

All twenty-eight rows describe the same energy. Thermal conventions and prefix capitalization remain explicit; complete copying and CSV retain every row when the table is hidden.

The same energy quantity in twenty-eight named conventions
Energy conventionConverted energy
Joules3600000.00000 J3600000.00000\,\mathrm J
Kilojoules3600.00000000 kJ3600.00000000\,\mathrm{kJ}
Thermochemical calories≈ 860420.650096 calth\approx\,860420.650096\,\mathrm{cal}_{\mathrm{th}}
Thermochemical kilocalories (food Calorie convention)≈ 860.420650096 kcalth\approx\,860.420650096\,\mathrm{kcal}_{\mathrm{th}}
Watt-hours1000.00000000 W h1000.00000000\,\mathrm{W\,h}
Kilowatt-hours1.00000000000 kW h1.00000000000\,\mathrm{kW\,h}
British thermal units (International Table)≈ 3412.14163313 BtuIT\approx\,3412.14163313\,\mathrm{Btu}_{\mathrm{IT}}
Electronvolts≈ 2.24694326681×1025 eV\approx\,2.24694326681\times10^{25}\,\mathrm{eV}
Foot-pound-force (work)≈ 2655223.73740 ft lbf\approx\,2655223.73740\,\mathrm{ft\,lbf}
Megajoules3.60000000000 MJ3.60000000000\,\mathrm{MJ}
Gigajoules0.00360000000000 GJ0.00360000000000\,\mathrm{GJ}
Terajoules3.60000000000×10−6 TJ3.60000000000\times10^{-6}\,\mathrm{TJ}
Millijoules (lowercase m)3.60000000000×109 mJ3.60000000000\times10^{9}\,\mathrm{mJ}
Microjoules3.60000000000×1012 μJ3.60000000000\times10^{12}\,\mathrm{\mu J}
Nanojoules3.60000000000×1015 nJ3.60000000000\times10^{15}\,\mathrm{nJ}
Ergs3.60000000000×1013 erg3.60000000000\times10^{13}\,\mathrm{erg}
Megawatt-hours0.00100000000000 MW h0.00100000000000\,\mathrm{MW\,h}
Gigawatt-hours1.00000000000×10−6 GW h1.00000000000\times10^{-6}\,\mathrm{GW\,h}
Watt-seconds3600000.00000 W s3600000.00000\,\mathrm{W\,s}
International Table calories≈ 859845.227859 calIT\approx\,859845.227859\,\mathrm{cal}_{\mathrm{IT}}
International Table kilocalories≈ 859.845227859 kcalIT\approx\,859.845227859\,\mathrm{kcal}_{\mathrm{IT}}
Kiloelectronvolts≈ 2.24694326681×1022 keV\approx\,2.24694326681\times10^{22}\,\mathrm{keV}
Megaelectronvolts≈ 2.24694326681×1019 MeV\approx\,2.24694326681\times10^{19}\,\mathrm{MeV}
Gigaelectronvolts≈ 2.24694326681×1016 GeV\approx\,2.24694326681\times10^{16}\,\mathrm{GeV}
Teraelectronvolts≈ 2.24694326681×1013 TeV\approx\,2.24694326681\times10^{13}\,\mathrm{TeV}
Inch-pound-force (work)≈ 3.18626848488×107 in lbf\approx\,3.18626848488\times10^{7}\,\mathrm{in\,lbf}
Kilogram-force meters (work)≈ 367097.836672 kgf m\approx\,367097.836672\,\mathrm{kgf\,m}
Million International Table Btu≈ 0.00341214163313 106 BtuIT\approx\,0.00341214163313\,10^6\,\mathrm{Btu}_{\mathrm{IT}}

Step-by-step energy calculation

  1. 1. Normalize the named energy convention

    Multiply the entered signed quantity by the exact joule factor. Thermochemical calories, IT calories and IT Btu remain explicitly named conventions.

    EJ=3600000.00000 JE_{\mathrm J}=3600000.00000\,\mathrm J

  2. 2. Divide by the destination energy factor

    Use the unrounded joule quantity for the selected destination and every comparison row. Display significant figures affect presentation, not the underlying energy model.

    Et=3600000.00000 JE_t=3600000.00000\,\mathrm J
What Can You Create?

Compare energy conventions and account for elapsed power

Translate an energy specification

Compare joules, watt-hours, thermal units, particle-scale energy and mechanical work using explicitly named factors. Prefix capitalization and calorie conventions remain visible in the selected result and the full table.

Model constant or average power

State both power and the elapsed duration to form an energy quantity. Normalized watts and seconds stay beside the result, making it clear which operating assumptions produced the modeled energy.

Check flat-rate energy-charge arithmetic

Apply your own rate per kilowatt-hour to the same energy quantity. Keep this separate arithmetic estimate and its exclusions with the physical conversion, rather than treating it as a complete utility bill.

Energy formulas and step-by-step examples

For direct entry, multiply by the named joule factor and divide by the destination factor. Here EsE_s is the entered number, while fsf_s and ftf_t are the joules represented by one source or target unit.

EJ=Esfs,Et=EJftE_{\mathrm J}=E_s f_s,\qquad E_t=\frac{E_{\mathrm J}}{f_t}

Convert one kilowatt-hour into joules

First identify the power prefix, then convert the hour into seconds. Both factors are exact. Their product explains why the original default is an energy quantity rather than a power rating.

1 kW h=1000 W×3600 s=3600000 J=3.6 MJ1\,\mathrm{kW\,h}=1000\,\mathrm W\times3600\,\mathrm s=3600000\,\mathrm J=3.6\,\mathrm{MJ}

Integrate a constant power over an elapsed interval

For a stated constant input power of 1500 W1500\,\mathrm W over 2 h2\,\mathrm h, normalize the time first. The same result follows if the supplied power is the actual time-average over that complete interval.

t=2×3600 s=7200 s,E=Pt=1500×7200 J=10800000 J=3 kW ht=2\times3600\,\mathrm s=7200\,\mathrm s,\qquad E=Pt=1500\times7200\,\mathrm J=10800000\,\mathrm J=3\,\mathrm{kW\,h}

Keep thermal definitions separate

The thermochemical small calorie and International Table small calorie use different definitions. A kilocalorie multiplies its own small-calorie convention by one thousand, so a prefix does not remove the need to identify the thermal standard.

1 calth=4.184 J,1 calIT=4.1868 J1\,\mathrm{cal}_{\mathrm{th}}=4.184\,\mathrm J,\qquad1\,\mathrm{cal}_{\mathrm{IT}}=4.1868\,\mathrm J

Apply a user-entered flat energy rate

At an entered rate of 0.200.20 currency units per kilowatt-hour, the modeled three-kilowatt-hour quantity gives the arithmetic below. This does not include any additional tariff component or establish a complete charge.

C=EkW hr=3×0.20=0.60 currency unitsC=E_{\mathrm{kW\,h}}r=3\times0.20=0.60\,\mathrm{currency\ units}
Why Users Love This Tool

Use named standards and retain the calculation assumptions

Definitions are traceable

  • All nine original energy identifiers and the one-kilowatt-hour example are preserved.
  • Thermochemical and International Table calories use separate exact factors.
  • Current electronvolt prefixes use the fixed elementary charge, while mechanical work is distinguished from torque.

Numerical precision stays reviewable

  • Exact rational arithmetic avoids intermediate rounding during conversion, power integration and rate multiplication.
  • Lossless numerical swaps preserve the same energy rather than starting from a rounded display.
  • Complete records retain every convention, optional model context and hidden working, with accessible mathematical rendering.
Perfect For

Built for energy specifications, learning and consumption notes

Electricity and device comparisons

Translate stated watt-hour capacities or calculate a supplied average input power over an elapsed interval. Match the input to the same physical boundary before comparing a battery label, device estimate or meter reading.

Thermal and mechanical reference work

Check the exact calorie or Btu convention and distinguish mechanical work from moment of force. Keep a source specification nearby when a shortened label leaves its thermal standard or physical quantity ambiguous.

Students following dimensional reasoning

Inspect how a watt multiplied by a second forms a joule, and how a decimal prefix changes the factor. Compare tiny electronvolt quantities with macroscopic units without losing the unrounded numerical model.

How It Works

How it works in three quick steps.

1

Identify the energy quantity or power-time model

Choose direct energy entry and select its named convention, or enter constant or time-average power and a nonnegative elapsed duration. Signed energy or power follows a transfer direction you declare.

2

Inspect the destination, factors and optional charge

Choose the destination energy convention and display significant figures. Review normalized joules, kilowatt-hours and the working. Optionally enter a nonnegative flat rate in your own currency units per kilowatt-hour to calculate energy-charge arithmetic.

3

Save the complete energy context

Copy the full record or LaTeX working, download all unit rows as CSV, share validated active settings or print the selected report to PDF. Retain thermal conventions, elapsed-time assumptions and any charge exclusions with your result.

Download & Print

Download and print a complete energy-conversion record

Copy the record or LaTeX working

Copy plain text with all factors and active assumptions, or copy properly delimited LaTeX steps. A versioned share link retains validated source choices, power-time inputs, rate options and report preferences.

Download all energy rows as CSV

The quoted UTF-8 file contains all twenty-eight energy conventions and exact numerical certificates, including hidden working. Model power, elapsed time and optional charge exclusions remain attached to the same calculation.

Print the selected report or save PDF

Choose the visible table, exact-ratio and working sections, then open the browser print dialog. Use portrait paper and check its preview. Controls and the supporting article are omitted; the numerical report retains model and charge assumptions. Very long ratios remain available in complete text and CSV.

FAQ

Frequently Asked Questions

How many joules are in a kilowatt-hour?
One kilowatt-hour is exactly 3.6×106 J3.6\times10^6\,\mathrm J. A kilowatt contributes a factor of one thousand relative to a watt, and an hour contributes a factor of three thousand six hundred relative to a second. Their product supplies the energy factor. The default example preserves this relationship directly, while the table also expresses the same quantity in megajoules, watt-hours, named calories and other energy conventions. Display rounding never changes the underlying exact numerical quantity.
Can I convert kilowatts into kilowatt-hours directly?
A kilowatt measures power, while a kilowatt-hour measures energy. An elapsed interval is needed to connect them. For constant power, or the time-average power over that interval, E=PtE=Pt. Select the power-time entry method and provide both inputs explicitly. A device nameplate power rating is not automatically its average consumption, and this converter does not infer a duty cycle, standby use, efficiency or operating schedule. A watt-hour must also not be confused with a watt per hour, which describes a different relationship.
Are a calorie, a kilocalorie and a food Calorie interchangeable?
A small calorie and a kilocalorie differ by a factor of one thousand. This page adopts the thermochemical kilocalorie for its clearly labeled food Calorie convention, with 1 kcalth=4184 J1\,\mathrm{kcal}_{\mathrm{th}}=4184\,\mathrm J. International Table calories and kilocalories are separate menu choices and use a different factor. A bare calorie label can therefore hide both a prefix ambiguity and a thermal convention. Confirm the intended meaning in the source before comparing numbers; capitalization and the full unit label matter.
Which British thermal unit does this converter use?
The Btu choice explicitly means the International Table convention, for which 1 BtuIT=1055.05585262 J1\,\mathrm{Btu}_{\mathrm{IT}}=1055.05585262\,\mathrm J exactly. The additional million-Btu entry is exactly one million of those same units. Other Btu conventions exist, including thermochemical and temperature-specific variants, so a bare Btu label should be checked before high-precision comparison. This page preserves the original Btu identifier while making its IT meaning visible, rather than silently substituting another thermal definition or relying on an ambiguous abbreviated prefix.
Is the electronvolt-to-joule factor exact?
For the current SI definition, 1 eV=1.602176634×10−19 J1\,\mathrm{eV}=1.602176634\times10^{-19}\,\mathrm J exactly because the elementary charge has a fixed numerical value. Older conversion tables may contain rounded or historical values, so this page uses the current constant rather than copying an older shortened factor. Kiloelectronvolts, megaelectronvolts, gigaelectronvolts and teraelectronvolts apply their stated decimal prefixes to that same definition. Exact unit arithmetic does not remove uncertainty from an experimentally measured particle energy or improve the precision of its original input.
What power and duration should I enter for an appliance?
Enter the constant input power, or its time-average over the complete elapsed interval being modeled. Choose the power convention explicitly and enter the elapsed interval independently. If consumption varies, an appropriate measured average or a sum of separately calculated operating intervals is needed. Fixed elapsed days contain twenty-four hours here and do not infer a local calendar transition. Output power, input power and a nameplate maximum are not automatically interchangeable; the calculation does not supply equipment efficiency, electrical power factor or a duty cycle.
Can energy or power be negative, and is foot-pound energy the same as torque?
Signed energy can represent a change or a transfer under a sign convention you declare, and signed model power preserves that direction. The elapsed duration remains nonnegative. Foot-pound-force on this page denotes mechanical work through distance. A torque value is a separate quantity, even when related dimensional units appear similar; rotational work additionally requires angular displacement, such as W=τθW=\tau\theta for constant aligned torque with angle in radians. The converter does not relabel a bare torque reading as a supplied amount of energy.
Does the rate estimate produce a complete bill, and what do saved records retain?
The optional flat-rate calculation multiplies energy in kilowatt-hours by the nonnegative rate you enter in your own currency units. It excludes fixed fees, taxes, tiered rates, exchange rates, equipment losses and any billing policy. A negative result is a signed arithmetic difference, not an assured refund. Exact numerical certificates describe the entered model rather than guaranteeing a charge or a measurement. Complete text and CSV preserve every energy row, active power-time assumptions, charge exclusions and hidden working; PDF follows the selected visible sections, and share links restore validated active settings.
About This Tool

About this Energy Converter

The Toolarithm Energy Converter expresses a stated energy quantity using a different named convention. It preserves the original one-kilowatt-hour default and all nine original identifiers, while extending the choice of decimal prefixes, thermal standards, particle-energy units and work units. Every definition is normalized through joules. The resulting comparison describes the same numerical energy in different units, rather than changing its physical origin or supplying missing experimental information.

A useful energy comparison begins by identifying the quantity at the same system boundary. An electricity meter reading, a battery energy label, a thermal transfer and a mechanical work calculation may all be expressed in joules, but converting the units alone does not establish that their input assumptions are equivalent. The page therefore makes the energy convention explicit and avoids inferring efficiency, useful output, device operating behavior or a source specification from the magnitude of a number.

The alternative entry method forms an energy quantity from constant or time-average power and a stated elapsed duration. Those inputs are normalized independently to watts and seconds before multiplication. This route supports signed transfer conventions and a zero-duration boundary without silently inventing a finite elapsed time. Fixed elapsed days contain twenty-four hours, so a calendar date range or a daylight-saving transition must be resolved separately before it becomes an elapsed interval for this model.

The optional energy-rate section is intentionally a separate multiplication using kilowatt-hours and a user-entered flat rate. Its currency unit is the one chosen by the user; there is no exchange-rate lookup or inference about a provider contract. Complete records include the exclusions so that a numerical energy-charge estimate can be reviewed without being mistaken for a bill. Exact arithmetic documents the entered values and factors, while display significant figures remain a presentation preference.

Server-rendered defaults and accessible mathematical markup keep the initial calculation and guide usable before interactive code loads. Edited results use the same mathematical report, and complete copying and CSV retain every unit row and active assumption. The printed record follows the chosen visible sections and keeps very long rational certificates in complete exports. Across these views, the converter keeps energy, power and torque conceptually separate and preserves the unrounded numerical model for later inspection.

Editorial Transparency

Who maintains this page

Ownership and review

Written and maintained by the Toolarithm editorial team. No review date is shown without a maintained editorial record. No independent professional review is claimed.

Methodology

Conversion factors are normalized to canonical units and checked in both directions. Exact definitions and offset formulas are preferred over rounded lookup values.

Read the editorial methodology

Dates and sources

Review dates change only after a substantive method or content check.

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