# Joule The **joule** (symbol **J**) is the SI derived unit of [[Energy|energy]], [[Work_(physics)|work]] and quantity of [[Heat|heat]]. One joule is the work done when a force of one newton moves its point of application one metre in the direction of the force, "when the motion is aligned with the direction of force," so that 1 J = 1 N·m.[^murphy-work] It is also one [[Watt|watt]] delivered for one second and one coulomb moved through one volt, and in base units it is one kilogram metre squared per second squared. The joule is a small unit by domestic standards: pushing with 2 N through half a metre, or with 0.1 N through ten metres, does one joule of work either way.[^murphy-work] In the microsim below the reader drives a single logarithmic power slider from 1 W to 10 MW, with a default of 100 W, and a simulated day plays out. An odometer accumulates E = P·t and reads the running total simultaneously in joules, kilowatt-hours, kilocalories, British thermal units, therms and [[Electronvolt|electronvolts]], using 1 kWh = 3.6×10⁶ J, 1 kcal = 4,184 J, 1 Btu ≈ 1,055 J and 1 therm = 1.055×10⁸ J.[^murphy-units] Marks along the axis sit at 97 W (an adult eating 2,000 kcal a day), at 1,440 W and 1,920 W (the derated limits of a 15 A and a 20 A household circuit at 120 V) and at 10 kW (the average share of the United States' total energy use per resident), and a second readout gives how long a 4.5 W·h battery would last at whatever power is selected.[^murphy-diet][^murphy-breakers] On the [[Energy]] flagship this article is the child of Part III — Units of measure, section *Units of measure* (row E12), the page that fixes the arithmetic every other section on the spine is quoted in. ## Definition The joule is defined as the work done by a force of one newton acting through a distance of one metre, which makes it a derived rather than a base unit: J = N·m = kg·m²·s⁻². Because the newton is itself kg·m·s⁻², every other expression of the joule follows from the same base quantities. One watt-second is one joule, since the [[Watt|watt]] is one joule per second.[^murphy-power] One coulomb-volt is one joule, because the electrical work done in moving a charge q through a potential difference V is E = q·V, and one ampere is one coulomb per second, which is why [[Electric_power|electrical power]] is P = I·V.[^murphy-electrical] One pascal-cubic-metre is one joule, since pressure times volume has the dimensions of energy — the fact that makes P·dV work in thermodynamics. Since the 2019 revision of the SI, the joule inherits its magnitude from a fixed numerical value of the [[Planck_constant|Planck constant]], h = 6.62607015×10⁻³⁴ J·s exactly, which defines the kilogram once the second and the metre are fixed.[^bipm-si] The practical consequence is that the joule no longer depends on any artefact, and that every energy measurement is ultimately traceable to frequency, the quantity metrology measures best. ## History The unit is named for James Prescott Joule, the Manchester brewer and experimenter who established that a definite quantity of mechanical work always produces a definite quantity of heat. Through the 1840s he measured the temperature rise produced by a falling weight turning a paddle wheel in an insulated vessel, arriving at the [[Mechanical_equivalent_of_heat|mechanical equivalent of heat]]; his mature account was published by the Royal Society in 1850.[^joule1850] The result was the empirical foundation of [[Conservation_of_energy|energy conservation]] and of [[Thermodynamics|thermodynamics]]: heat and work are not different substances but different routes for the same quantity, and the exchange rate between them is fixed. Joule's name was attached to the unit of work by international agreement in the closing years of the nineteenth century, and the joule was carried into the International System of Units when the SI was established in 1960.[^bipm-si] The calorie, defined as the heat needed to raise one gram of water by one degree Celsius, survived alongside it and still dominates nutrition; the modern definition simply fixes it against the joule, at 1 cal = 4.184 J.[^murphy-cal] [[Joule_heating|Joule heating]], the dissipation of electrical energy as heat in a resistance at a rate P = I²·ρ·ℓ/A, carries his name as well.[^mitofsky-joule] ## Practical examples The joule is best learned as an odometer reading rather than a definition, which is what the microsim is for: power is the speedometer, energy the odometer, and E = P·t is the only equation in the panel.[^murphy-power] Work through a distance supplies the first calibration points — 2 N through 0.5 m and 0.1 N through 10 m each give 1 J, and 150 N through 5 m gives 750 J.[^murphy-work] Lifting a 10 kg box, weighing about 100 N, through 2 m takes roughly 200 J; done in one second that is 200 W, done over four seconds it is 50 W, and the energy is the same either way.[^murphy-power] The marks on the slider are chosen to be memorable. An adult eating 2,000 kcal a day is metabolising 8.368 MJ over 86,400 s, an average of 96.85 W — "very close to 100 W", and a figure the source warns should not be quoted to four significant figures.[^murphy-diet] Household circuits give the next rungs: a 15 A and a 20 A breaker at 120 V are nominally 1,800 W and 2,400 W, but continuous loads are derated to 80 %, so the honest limits are about 1,440 W and 1,920 W, and the sim draws the derated line rather than the nominal one.[^murphy-breakers] The top mark is the average resident of the United States at roughly 10,000 W, which is about a hundred people's worth of [[Food_energy|food energy]] and, at that rate, 240 kWh a day (derived).[^murphy-scale] The battery readout uses a 9 V cell rated at 0.5 A·h, which holds 4.5 W·h or 16.2 kJ and therefore runs for 4.5 hours at 1 W.[^murphy-battery] Two cautions travel with the panel. The reference values populating its axis are explicitly illustrative rather than definitive, so the sim rounds them and shows ranges instead of implying precision they do not have — this table is ILLUSTRATIVE in the strict sense, a display of magnitudes and not a set of measurements.[^murphy-table51] And food energy and water heating share units without sharing physics: the same 40 kcal that raises 2 kg of water by 20 °C is not interchangeable with 40 kcal of diet in any accounting that matters.[^murphy-cal] ## Multiples Because the joule is small, real quantities are quoted with SI prefixes, and the spread is enormous. A single visible-light [[Photon|photon]] carries about 5×10⁻¹⁹ J; a chemical bond is a few times that; a domestic meal is megajoules; a day of national electricity supply is petajoules. The quad, defined as 10¹⁵ Btu, sits near the top at 1.055×10¹⁸ J, and it is the unit in which national energy budgets are usually discussed: the United States uses roughly 100 quads a year, which averaged over a year of about 3.16×10⁷ seconds is close to 3 TW.[^murphy-scale] The lower end has its own unit. One [[Electronvolt|electronvolt]], the energy an electron gains falling through one volt, is 1.6×10⁻¹⁹ J, and it is the natural currency of atomic and chemical processes because valence-electron energies are of that order.[^murphy-ev] The therm, 10⁵ Btu or 1.055×10⁸ J, occupies the domestic gas-supply niche between the two, and the quad is exactly 10¹³ therms (derived). Spanning from the electronvolt to the quad is thirty-seven orders of magnitude, which is why the microsim's power axis is logarithmic and why converting between the conventional units of different industries is a routine source of error. ## Conversions Every unit in common use can be written as a fixed multiple of the joule, and the microsim's readout is simply the odometer value divided through by each of them in turn. | Unit | In joules | Where it is used | |---|---|---| | kilowatt-hour (kWh) | 3.6×10⁶ J | electricity billing[^murphy-units] | | calorie (cal) | 4.184 J | thermochemistry[^murphy-cal] | | kilocalorie (kcal, "Calorie") | 4,184 J | nutrition[^murphy-cal] | | British thermal unit (Btu) | ≈1,055 J | heating and cooling loads[^murphy-units] | | therm | 10⁵ Btu = 1.055×10⁸ J = 29.3 kWh | natural-gas supply[^murphy-therm] | | quad | 10¹⁵ Btu ≈ 1.055×10¹⁸ J | national energy statistics[^murphy-units] | | electronvolt (eV) | 1.6×10⁻¹⁹ J | atomic and chemical energies[^murphy-ev] | | watt-hour (W·h) | 3,600 J | battery capacity, as A·h × V[^murphy-battery] | Two conversion rates that are not energies but appear beside them: one horsepower is 745.7 W, so 100 hp is about 75 kW, and one Btu per hour is 0.293 W, so a 30,000 Btu/hr appliance draws 8,800 W.[^murphy-power][^murphy-units] The [[Units_of_energy|energy units]] of the gas industry are volumetric rather than thermal and need a conversion factor of their own: 100 ft³ of [[Natural_gas|natural gas]] carries about 1.036 therm and a gallon of propane about 91,500 Btu, so 10,000 kcal of cooking is 41.84 MJ, about 40,000 Btu, 0.4 therm, roughly 40 ft³ of gas, or a little under half a gallon of propane.[^murphy-therm] National figures can be cross-checked the same way: 4×10¹² kWh of United States electricity is 13.6 quads (derived), consistent with the roughly 14 quads reported for 2010.[^kerlin-quads] ## Newton-metre and torque The newton-metre is dimensionally identical to the joule, yet the two name different physical quantities and are deliberately not interchanged. Work is the scalar product of force and displacement, so the newton and the metre point along the same line and the result is an energy in joules. [[Torque|Torque]] is the cross product of a position vector and a force, so the newton and the metre are perpendicular and the result is a vector quantity whose magnitude is quoted in newton-metres, never in joules. The distinction matters as soon as rotation does work. Turning through an angle θ under a torque τ delivers W = ∫τ·dθ, and since the radian is dimensionless the integral comes out in joules — so torque in newton-metres multiplied by angle in radians gives energy in joules, and the unit name changes at the point where the quantity does. The same care is needed with the pascal-cubic-metre in a P·dV term and with the volt-ampere in alternating-current power, where identical dimensions carry different physical meanings and different conventional names. ## Watt-second The watt-second is the joule under another name, and it exists because electrical engineering finds it natural to start from power rather than from force. One [[Watt|watt]] is one joule per second, so the product of watts and seconds returns joules exactly; scaling both factors gives the kilowatt-hour, 1,000 J/s multiplied by 3,600 s, which is 3.6 MJ.[^murphy-units] That is the unit on every domestic electricity bill, and the conversion is the single most useful number in the whole ladder. The corresponding trap is a unit that does not exist. Energy is power multiplied by time, so "kilowatts per hour" is never a quantity of anything; the correct form is always the kilowatt-hour, and the microsim's readout is labelled to make the multiplication explicit.[^murphy-power] Battery capacity has a parallel convention: ampere-hours are a charge, and only after multiplying by the cell voltage do they become watt-hours and therefore joules — 0.5 A·h at 9 V is 4.5 W·h, or 16.2 kJ.[^murphy-battery] Both conventions are survivals from an era when [[Electric_current|current]] and [[Voltage|voltage]] were metered separately, and both are still the form in which the numbers arrive. *See also:* [[Kilowatt-hour]] · [[Electronvolt]] · [[Watt]] · [[Power_(physics)]] · [[British_thermal_unit]] · [[Units_of_energy]] · [[Calorie]] ## References [^murphy-work]: Murphy, Thomas (2021). *Energy and Human Ambitions on a Finite Planet*. Chapter 5 "Energy and Fossil Fuels", pp. 88–89 (W = F·d "when the motion is aligned with the direction of force"; 1 J = 1 N·m; Table 5.1's worked pairs, including 2 N × 0.5 m = 1 J, 0.1 N × 10 m = 1 J and 150 N × 5 m = 750 J). Portal Book 097, https://open.umn.edu/opentextbooks/textbooks/energy-and-human-ambitions-on-a-finite-planet [^murphy-power]: Murphy (2021), *Energy and Human Ambitions on a Finite Planet*, Chapter 5, pp. 91–93 (1 W = 1 J/s; a 10 kg box lifted 2 m takes ≈200 J, which is 200 W in 1 s or 50 W in 4 s; 1 hp = 745.7 W and 100 hp ≈ 75 kW; power is the speedometer and energy the odometer; never label anything "kW per hour"). Portal Book 097. [^murphy-units]: Murphy (2021), *Energy and Human Ambitions on a Finite Planet*, Chapter 5, pp. 92–95 (1 kWh = 1,000 J/s × 3,600 s = 3.6 MJ; 1 Btu ≈ 1,055 J; 1 quad ≈ 1.055×10¹⁸ J; 1 Btu/hr = 0.293 W; 30,000 Btu/hr = 8,800 W). Portal Book 097. [^murphy-cal]: Murphy (2021), *Energy and Human Ambitions on a Finite Planet*, Chapter 5, pp. 93–95 (1 cal = 4.184 J and 1 kcal = 4,184 J; 40 kcal raises 2 kg of water by 20 °C; food energy and water heating share units but not physics). Portal Book 097. [^murphy-therm]: Murphy (2021), *Energy and Human Ambitions on a Finite Planet*, Chapter 5, p. 96 (1 therm = 10⁵ Btu = 1.055×10⁸ J = 29.3 kWh; 100 ft³ of natural gas ≈ 1.036 therm; 1 gal of propane ≈ 91,500 Btu; 10,000 kcal = 41.84 MJ ≈ 40,000 Btu = 0.4 therm ≈ 40 ft³ of gas). The quad = 10¹³ therms identity is derived. Portal Book 097. [^murphy-electrical]: Murphy (2021), *Energy and Human Ambitions on a Finite Planet*, Chapter 5, p. 97 (E = q·V as Eq. 5.1; 1 A = 1 C/s; P = I·V as Eq. 5.2; A·h × V = W·h). Portal Book 097. [^murphy-ev]: Murphy (2021), *Energy and Human Ambitions on a Finite Planet*, Chapter 5, pp. 98–99 (1 eV = 1.6×10⁻¹⁹ J as Eq. 5.3; photon energy E = h·ν = h·c/λ with h = 6.626×10⁻³⁴ J·s, and visible light at 0.4–0.7 µm carrying 5.0–2.8×10⁻¹⁹ J, or 3.1–1.8 eV). Portal Book 097. [^murphy-diet]: Murphy (2021), *Energy and Human Ambitions on a Finite Planet*, Chapter 5, pp. 94–95 (2,000 kcal/day = 8.368 MJ over 86,400 s = 96.85 W, "very close to 100 W", with the book's own warning that quoting it to four figures is false precision). Portal Book 097. [^murphy-breakers]: Murphy (2021), *Energy and Human Ambitions on a Finite Planet*, Chapter 5, p. 97 (15 A and 20 A breakers at 120 V give 1,800 W and 2,400 W nominal, with an 80 % continuous-use derating; the book rounds the derated 15 A figure to ≈1,400 W, while 0.8 × 1,800 = 1,440 W). Portal Book 097. [^murphy-scale]: Murphy (2021), *Energy and Human Ambitions on a Finite Planet*, Chapter 5, p. 95 (1 yr ≈ 3.16×10⁷ s; the United States uses ≈100 quads/yr ≈ 3 TW ≈ 10,000 W per person). The 240 kWh per day per person is derived. Portal Book 097. [^murphy-battery]: Murphy (2021), *Energy and Human Ambitions on a Finite Planet*, Chapter 5, p. 98 (a 9 V, 0.5 A·h battery holds 4.5 W·h = 16.2 kJ, or 4.5 h at 1 W). Portal Book 097. [^murphy-table51]: Murphy (2021), *Energy and Human Ambitions on a Finite Planet*, Chapter 5, pp. 89 and 92 (Table 5.1's activity–energy pairs and Fig. 5.2's power reference points are described as illustrative, "not definitive or exact"). Portal Book 097. [^kerlin-quads]: Kerlin, Thomas (2013). *Future Energy: Opportunities & Challenges*. Chapter 5, p. 221, and Chapter 6, p. 246 (United States electricity at ≈14 quads for 2010 and ≈4 trillion kWh/yr). The 13.6 quad cross-check is derived. Portal Book 048, https://open.umn.edu/opentextbooks/textbooks/future-energy-opportunities-challenges [^mitofsky-joule]: Mitofsky, Andrea (2018). *Direct Energy*. Part II "Theoretical Ideas", p. 201 (Joule heating, P = I²·ρ·ℓ/A; 3 mA through a 1 mm length of 1 mm² cross-section at ρ = 10⁻⁵ Ω·m dissipates 9×10⁻⁸ W). Portal Book 055, https://open.umn.edu/opentextbooks/textbooks/direct-energy [^joule1850]: Joule, James Prescott (1850). "On the Mechanical Equivalent of Heat." *Philosophical Transactions of the Royal Society of London*, volume 140. [^bipm-si]: Bureau International des Poids et Mesures (2019). *The International System of Units (SI)*, 9th edition (the joule as an SI derived unit with special name, J = N·m = kg·m²·s⁻²; the defining constant h = 6.62607015×10⁻³⁴ J·s; the SI established in 1960). ## External links - [Energy and Human Ambitions on a Finite Planet](https://open.umn.edu/opentextbooks/textbooks/energy-and-human-ambitions-on-a-finite-planet), Thomas Murphy — Chapter 5 is the unit ladder this article is built on, Portal Book 097 - [Future Energy: Opportunities & Challenges](https://open.umn.edu/opentextbooks/textbooks/future-energy-opportunities-challenges), Thomas Kerlin — quads and national electricity figures, Portal Book 048 - [Direct Energy](https://open.umn.edu/opentextbooks/textbooks/direct-energy), Andrea Mitofsky — Joule heating and direct conversion, Portal Book 055 - The Wikipedia pair's external links list the standards bodies' own definitions <!-- MATTERSIM:BEGIN g24 — Matter & Energy Cluster microsim (framework build, specs/sims/Joule.json); do not hand-edit inside --> **Microsim — three.js (Wikitube framework), pending deploy:** *Joule* will play here once `https://wikitube-3d-microsims.netlify.app/matter/Joule.html` is live. <!-- pending: <div class="wt-sim" data-src="https://wikitube-3d-microsims.netlify.app/matter/Joule.html" data-title="Joule"></div> --> <!-- MATTERSIM:END --> ## Wikipedia : Wikitube **Strict pair:** [Wikipedia](https://en.wikipedia.org/wiki/Joule) : [Wikitube](https://en.wikitube.io/wiki/Joule) · pinned revision [1373502212](https://en.wikipedia.org/w/index.php?oldid=1373502212) · 2026-09-11 ## Previous hub tags Hubs: `Life_Physics`. Portals: [[PORTAL_Energy]]. --- *Matter & Energy Cluster child articles, wave 1 · 2026-09-11 · drafted · Energy row E12 · sim pending (matter/Joule).*