⚡ Energy Conversion Calculator
Convert between Joule, BTU, kWh, Calorie, eV, MJ, ft·lb, erg, therm, ton TNT and 60+ energy units — with work-energy theorem, thermodynamic laws, E=mc², kWh billing, nuclear & heat energy formulas rendered in MathJax
🔄 Energy Unit Converter
🌍 All Units at Once
📖 How to Use This Energy Conversion Calculator
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1Filter by Energy Category (Optional)
Click SI/Joules (J, kJ, MJ, GJ, erg), Thermal (BTU, calorie, therm, CHU), Electrical (Wh, kWh, MWh, TWh), Mechanical (ft·lb, hp·h, kgf·m), Fuel (toe, tce, gasoline, diesel), or Atomic/Nuclear (eV, MeV, ton TNT) to narrow dropdowns.
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2Enter Your Energy Value
Type the value into "Enter Value." Accepts any numeric input — from femtojoules (laser pulses) to exajoules (national energy statistics). Scientific notation auto-applies for extreme values.
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3Select From and To Units
Choose your source unit in "From Unit" and target in "To Unit." The result and exact conversion factor appear instantly in the rose result box.
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4Use Quick-Convert Buttons
Click preset buttons — J↔BTU, kWh↔J, kcal→J, kWh→BTU, eV→J — for the most common energy conversions. Both dropdowns update automatically.
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5View All Units & Copy
"All Units at Once" displays your energy in every supported unit simultaneously. Click "📋 Copy Result" to copy the primary conversion for engineering calculations, energy billing, or coursework.
📐 Energy Unit Conversion Reference Table
| From | To | Multiply By | Mathematical Expression |
|---|---|---|---|
| 1 J | BTU | 0.000948 | \( 1\,\text{J} = 1/1055.06\,\text{BTU} \) |
| 1 BTU | J | 1,055.06 | \( 1\,\text{BTU} = 1055.06\,\text{J} \) |
| 1 kWh | J | 3,600,000 | \( 1\,\text{kWh} = 3.6 \times 10^6\,\text{J} \) |
| 1 kWh | BTU | 3,412.14 | \( 1\,\text{kWh} = 3{,}412.14\,\text{BTU} \) |
| 1 kcal (food) | J | 4,184 | \( 1\,\text{kcal} = 4{,}184\,\text{J} \) |
| 1 cal (IT) | J | 4.1868 | \( 1\,\text{cal} = 4.1868\,\text{J} \) |
| 1 MJ | kWh | 0.27778 | \( 1\,\text{MJ} = 1{,}000/3{,}600\,\text{kWh} \) |
| 1 therm (US) | kWh | 29.307 | \( 1\,\text{therm} = 10^5\,\text{BTU} = 105.48\,\text{MJ} \) |
| 1 eV | J | 1.602×10⁻¹⁹ | \( 1\,\text{eV} = 1.602176634 \times 10^{-19}\,\text{J} \) |
| 1 MeV | J | 1.602×10⁻¹³ | \( 1\,\text{MeV} = 10^6\,\text{eV} = 1.602 \times 10^{-13}\,\text{J} \) |
| 1 ft·lbf | J | 1.355818 | \( 1\,\text{ft·lbf} = 1.355818\,\text{J} \) |
| 1 ton TNT | GJ | 4.184 | \( 1\,\text{t TNT} = 4.184\,\text{GJ} \) |
⚡ Understanding Energy — A Complete Physics & Engineering Guide
Energy is one of the most fundamental and pervasive concepts in all of science. It underlies every physical process — from the chemical bonds that power living cells, to the electromagnetic radiation from the Sun, to the gravitational collapse of stars. Energy cannot be created or destroyed (the First Law of Thermodynamics); it can only be converted from one form to another. Understanding and accurately converting between energy units is therefore not just an academic exercise — it is essential for electrical billing, HVAC design, nutrition science, automotive fuel economy, nuclear engineering, and astrophysics.
The SI unit of energy is the joule (J). Depending on the application and national tradition, energy is also measured in: kilowatt-hours (electricity billing), BTU (HVAC and US gas ratings), calories and kilocalories (nutrition and chemistry), electronvolts (atomic and particle physics), ergs (CGS physics), foot-pounds (mechanical engineering), therms (natural gas utility billing), and tonnes of oil equivalent (international energy statistics). This calculator handles all of them — and more.
🔬 The Work-Energy Theorem & Conservation of Energy
The Work-Energy Theorem is the bedrock of classical mechanics — it states that the net work done on an object equals the change in its kinetic energy. This directly links force, distance, and energy in a single unifying relationship, and explains why converting between mechanical energy units (joules, foot-pounds, horsepower-hours) requires precise conversion factors.
\( W_{\text{net}} = \Delta KE = \tfrac{1}{2}mv_f^2 - \tfrac{1}{2}mv_i^2 \qquad \text{(Work-Energy Theorem)} \)
\( KE = \tfrac{1}{2}mv^2 \qquad PE_{\text{grav}} = mgh \qquad PE_{\text{spring}} = \tfrac{1}{2}kx^2 \)
\( E_{\text{mechanical}} = KE + PE = \text{constant} \qquad \text{(conservation, no friction)} \)
\( P = \frac{W}{t} = \frac{\Delta E}{\Delta t} \qquad W = P \times t \qquad [\,1\,\text{kWh} = 1\,\text{kW} \times 3600\,\text{s} = 3.6 \times 10^6\,\text{J}\,] \)
Problem: A 1,500 kg car brakes from 100 km/h (27.78 m/s) to rest. Calculate the kinetic energy dissipated in joules, kWh, BTU, and kcal.
Step 1 — KE in joules: \( KE = \frac{1}{2}mv^2 = \frac{1}{2} \times 1500 \times 27.78^2 = \frac{1}{2} \times 1500 \times 771.7 = \mathbf{578{,}793\,\text{J}} \approx 578.8\,\text{kJ} \)
kWh: \( 578{,}793 \div 3{,}600{,}000 = \mathbf{0.1608\,\text{kWh}} \)
BTU: \( 578{,}793 \div 1{,}055.06 = \mathbf{548.6\,\text{BTU}} \)
kcal (food): \( 578{,}793 \div 4{,}184 = \mathbf{138.4\,\text{kcal}} \)
Insight: The braking energy (~138 food Calories) is released as heat in the brake discs. Regenerative braking in electric vehicles converts this back to electrical energy stored in the battery — recovering up to 70% of kinetic energy in urban driving.
🔌 The Kilowatt-Hour — Electricity Billing & Energy Storage
The kilowatt-hour (kWh) is the commercial unit of electrical energy — the quantity you pay for on your electricity bill. It is defined as the energy consumed by a 1-kilowatt appliance running for exactly one hour. Despite not being an SI unit, the kWh is indispensable in energy economics, grid management, EV range specification, and solar panel sizing.
\( 1\,\text{kWh} = 1\,\text{kW} \times 1\,\text{h} = 1000\,\text{W} \times 3600\,\text{s} = 3{,}600{,}000\,\text{J} = 3.6\,\text{MJ} \quad \text{(exact)} \)
\( 1\,\text{kWh} = 3{,}412.142\,\text{BTU} = 859.845\,\text{kcal} = 2655.2\,\text{ft·lbf} \times 10^3 \)
\( E\,[\text{kWh}] = P\,[\text{kW}] \times t\,[\text{h}] \qquad \text{Cost} = E \times \text{tariff}\,[\$/\text{kWh}] \)
\( 1\,\text{MWh} = 1000\,\text{kWh} = 3.6\,\text{GJ} \qquad 1\,\text{TWh} = 10^9\,\text{kWh} = 3.6\,\text{PJ} \)
🔥 The British Thermal Unit (BTU) — Heating, Cooling & HVAC
The British Thermal Unit (BTU) is the amount of heat energy required to raise the temperature of exactly one avoirdupois pound (0.4536 kg) of liquid water by exactly 1°F (0.5556°C) at a specified temperature. Multiple definitions exist — the International Table (IT) BTU (1,055.06 J) is the most widely used in engineering. The BTU remains the dominant energy unit in US HVAC, refrigeration, heating equipment, and natural gas billing.
\( 1\,\text{BTU (IT)} = 1{,}055.05585262\,\text{J} \quad \text{(exact per ISO 31-4)} \)
\( 1\,\text{kWh} = 3{,}412.142\,\text{BTU} \qquad 1\,\text{therm} = 100{,}000\,\text{BTU} = 105.48\,\text{MJ} \)
\( Q = mc\Delta T \qquad \text{(heat energy: mass × specific heat × temperature rise)} \)
\( 1\,\text{BTU/h} = 0.293071\,\text{W} \qquad 1\,\text{ton of refrigeration} = 12{,}000\,\text{BTU/h} = 3.517\,\text{kW} \)
Problem: A gas boiler consumes 3.5 therms per day in winter. Convert to BTU, kWh, MJ, and estimate the daily energy cost at $1.20/therm.
BTU: \( 3.5 \times 100{,}000 = \mathbf{350{,}000\,\text{BTU}} \)
MJ: \( 350{,}000 \times 1{,}055.06 \div 10^6 = \mathbf{369.3\,\text{MJ}} \)
kWh: \( 369.3 \div 3.6 = \mathbf{102.6\,\text{kWh}} \)
Cost: \( 3.5 \times \$1.20 = \mathbf{\$4.20/\text{day}} \) for heating. Running the equivalent electric resistance heater at $0.15/kWh: \( 102.6 \times 0.15 = \$15.39/\text{day}\) — 3.7× more expensive, illustrating why natural gas dominates residential heating economics.
🍎 Calories & Kilocalories — Nutrition Energy
Few unit distinctions cause more confusion than the calorie vs. Calorie problem. There are actually multiple calorie definitions in scientific literature, and the food calorie is a completely different magnitude from the chemistry calorie — despite sharing the same name in casual usage.
\( 1\,\text{cal (IT)} = 4.1868\,\text{J} \quad \text{(International Table calorie)} \)
\( 1\,\text{cal (th)} = 4.184\,\text{J} \quad \text{(thermochemical calorie, used in chemistry)} \)
\( 1\,\text{Cal} = 1\,\text{kcal} = 1000\,\text{cal} = 4{,}184\,\text{J} = 3.968\,\text{BTU} \quad \text{(food Calorie)} \)
\( Q = mc\Delta T \qquad c_{\text{water, IT}} = 4{,}186.8\,\text{J/(kg·K)} = 1\,\text{kcal/(kg·°C)} \)
⚛️ Electronvolt (eV) — Atomic, Particle & Nuclear Physics
The electronvolt (eV) is the energy unit of atomic and particle physics. It is defined as the kinetic energy gained by a single electron (charge e = 1.602176634×10⁻¹⁹ C) when accelerated through an electric potential difference of exactly one volt. This makes it extraordinarily small — roughly 160 zeptojoules — but perfectly scaled for the energies of individual photons, atomic transitions, and chemical bonds.
\( 1\,\text{eV} = 1.602176634 \times 10^{-19}\,\text{J} \quad \text{(exact — SI 2019 redefinition)} \)
\( 1\,\text{MeV} = 10^6\,\text{eV} = 1.602 \times 10^{-13}\,\text{J} \qquad 1\,\text{GeV} = 10^9\,\text{eV} \)
\( E = mc^2 \qquad c = 299{,}792{,}458\,\text{m/s} \quad \text{(Einstein's mass-energy equivalence)} \)
\( 1\,\text{u} = 931.494\,\text{MeV/c}^2 \qquad \text{proton rest energy} = 938.272\,\text{MeV} \)
\( \text{Uranium-235 fission: } \approx 200\,\text{MeV/nucleus} = 8.2 \times 10^{13}\,\text{J/kg} \qquad \text{vs. coal: } 3.3 \times 10^7\,\text{J/kg} \)
🌍 Real-World Energy Reference Table
| Event / Object | Joules (J) | kWh | Notes |
|---|---|---|---|
| 🔦 Single visible photon | ~3×10⁻¹⁹ | ~8×10⁻²⁶ | ~1.9 eV (green light, 520 nm) |
| 🪫 AA battery (alkaline) | ~9,000 | 0.0025 | 1.5 V × ~2 Ah × 3,600 = 10.8 kJ |
| 🔌 1 kWh (electricity bill unit) | 3,600,000 | 1 | = 3.6 MJ = 3,412 BTU |
| 🚗 Tank of petrol (50 L) | ~1.71×10⁹ | ~475 | 34.2 MJ/L × 50 L |
| 🍎 Daily food intake (2,000 Cal) | ~8.37×10⁶ | 2.33 | 2,000 kcal × 4,184 J/kcal |
| 💣 Hiroshima bomb | ~6.3×10¹³ | ~17.5×10⁶ | ~15 kilotons TNT equivalent |
| 🌋 Krakatau eruption (1883) | ~8.4×10¹⁸ | ~2.3×10¹² | ~200 megatons TNT estimated |
| 🌍 Global energy use (2023) | ~5.8×10²⁰ | ~1.6×10¹⁴ | ~580 EJ (IEA 2023 data) |
| ☀️ Solar energy hitting Earth/day | ~1.5×10²² | ~4.2×10¹⁵ | 1,361 W/m² × Earth disc area × 86,400 s |
📦 Energy Unit System Guide
Joule (J) — SI Universal
\(1\,\text{J} = 1\,\text{N·m} = 1\,\text{kg·m}^2\text{/s}^2 = 1\,\text{W·s}\). Universal in physics. 1 kJ = 1,000 J; 1 MJ = 10⁶ J. Links to force (N·m), power (W·s), and pressure (Pa·m³).
kWh — Commercial Energy
\(1\,\text{kWh} = 3.6\,\text{MJ}\). Standard for electricity billing worldwide. Battery capacity, solar output, EV range all measured in kWh. 1 TWh = nation-scale annual production.
BTU — US Thermal Engineering
\(1\,\text{BTU} = 1{,}055.06\,\text{J}\). HVAC equipment ratings, US natural gas, heating oil, air conditioner capacity. 1 therm = 100,000 BTU. 12,000 BTU/h = 1 ton of refrigeration.
eV — Atomic Physics
\(1\,\text{eV} = 1.602 \times 10^{-19}\,\text{J}\). Particle physics, photon energy, chemical bond energies, semiconductor band gaps. Proton mass-energy: 938.272 MeV.
🌡️ Laws of Thermodynamics — Energy Conversion in Context
\( \textbf{0th Law:} \quad \text{If } A = B \text{ and } A = C \text{ in thermal equilibrium, then } B = C \quad \text{(defines temperature)} \)
\( \textbf{1st Law:} \quad \Delta U = Q - W \quad \text{(energy conservation: internal energy = heat in − work out)} \)
\( \textbf{2nd Law:} \quad \Delta S \geq 0 \quad \text{(entropy of isolated system never decreases — no perpetual motion)} \)
\( \eta_{\text{Carnot}} = 1 - \frac{T_C}{T_H} \leq 1 \quad \text{(maximum efficiency of any heat engine)} \)
\( E = mc^2 \quad \text{(4th bridge — matter is concentrated energy)} \)