Physics unit conversions rewrite a measured quantity in different units without changing the quantity itself. You multiply by a conversion ratio — a fraction equal to 1, such as 1000 m / 1 km — so the unwanted unit cancels. Temperature is the exception: kelvin and degrees Celsius are separated by an additive offset of 273.15, not a factor.
Your car manual specifies 2.2 bar. The garage gauge reads psi. The tyre itself is stamped in kPa. Three numbers, three units, one physical quantity — and somewhere in that gap, people guess.
Physics runs on the same gap, only the stakes are higher. A joule and an electronvolt both measure energy, but they differ by nineteen orders of magnitude. Get the factor wrong and your answer is not slightly off; it is meaningless.
What Are Physics Unit Conversions?
A unit conversion changes the label on a measurement, never the measurement. Write 5 kg or 5000 g and you are describing the same lump of matter; only the yardstick changed.
That sounds obvious until you meet a unit that hides a second quantity inside it. A newton is not a fundamental thing — it is shorthand for kg·m/s2. An electronvolt smuggles in the elementary charge. A pascal is a newton spread over a square metre.
So conversions come in two flavours, and confusing them is where marks go missing:
- Scale conversions — multiply by a factor. Nearly everything: N to kN, J to eV, Pa to atm, m to miles.
- Affine conversions — multiply and shift. Only temperature scales that do not start at absolute zero, namely degrees Celsius and degrees Fahrenheit.
Everything else in this guide follows from knowing which one you are holding.
The Conversion-Ratio Method: One Rule Behind Every Conversion
Every scale conversion is a multiplication by a fraction that equals exactly 1. Because 1000 m and 1 km are the same length, the fraction 1000 m / 1 km has the value 1 — so multiplying by it changes the units on the page without touching the physical quantity.
Written as a chain, the units behave like algebra: anything appearing top and bottom cancels, and you keep multiplying ratios until only the unit you want survives.
The conversion-ratio method: stack fractions worth 1 until the unwanted units cancel.
Two habits make this reliable. Carry the units through every line rather than tracking numbers alone, and keep full precision until the very end — NIST’s guidance on unit conversion is explicit that you round once, on the final answer.
In practice, the cancelling is also your error-check. If you finish a chain and the leftover units are not the ones you wanted, you have flipped a ratio upside down — no need to hunt through the arithmetic.
SI Prefixes: The Conversions You Do Most Often
Prefix conversions are pure powers of ten, which is why they feel easy and get botched anyway. The prefix is part of the unit, so “k” always means the number 1000 sitting in front of whatever follows.
| Prefix | Symbol | Factor | Typical physics use |
|---|---|---|---|
| tera | T | 1012 | THz optical frequencies |
| giga | G | 109 | GeV particle energies |
| mega | M | 106 | MPa material stress |
| kilo | k | 103 | kN forces, kJ energies |
| centi | c | 10-2 | cm lengths, cm3 volumes |
| milli | m | 10-3 | mA currents, mm lengths |
| micro | μ | 10-6 | μF capacitance |
| nano | n | 10-9 | nm wavelengths |
| pico | p | 10-12 | pF capacitance |
| femto | f | 10-15 | fm nuclear radii |
The trap is prefixes on squared and cubed units, because the exponent hits the prefix too. Since 1 cm = 10-2 m, it follows that 1 cm3 = (10-2 m)3 = 10-6 m3 — a factor of a million, not a hundred.
That single slip is behind most density errors, which is why 1 g/cm3 equals 1000 kg/m3 rather than anything smaller. If you would rather not do the powers by hand, our SI Prefix Converter steps a value between any two prefixes and shows the exponent arithmetic.
Force Conversions: N, kN, dyne and Pound-Force
The newton is the SI unit of force, defined as the force that accelerates 1 kg at 1 m/s2. Everything in the table below is that same quantity wearing a different coat.
| Unit | Value in newtons | Exact? | Where you meet it |
|---|---|---|---|
| 1 kilonewton (kN) | 1000 N | Exact | Structural loads, rocket thrust |
| 1 millinewton (mN) | 0.001 N | Exact | Ion thrusters, surface tension |
| 1 dyne (dyn) | 10-5 N | Exact | Older CGS-unit papers |
| 1 kilogram-force (kgf) | 9.80665 N | Exact | Engineering, gym plates |
| 1 pound-force (lbf) | 4.4482 N | 4.448 221 615 260 5 N exactly | US aerospace and engineering |
Notice that the pound-force factor is exact rather than measured. It falls out of two defined numbers: the pound is exactly 0.453 592 37 kg, and standard gravity is exactly 9.806 65 m/s2.
Which raises the single most common force error. Kilograms measure mass; newtons measure force. On Earth a 1 kg mass weighs about 9.81 N, but that is a physics calculation using g, not a unit conversion — and the answer changes on the Moon while the mass does not. If that distinction feels shaky, our guide to the types of forces in physics works through weight as a force in detail.
Energy Conversions: J, eV, Calories and Kilowatt-Hours
Energy has the messiest unit zoo in physics, because chemists, electricians, nutritionists and particle physicists all invented their own. The joule ties them together: 1 J = 1 N·m = 1 kg·m2/s2.
| Unit | Value in joules | Exact? | Where you meet it |
|---|---|---|---|
| 1 electronvolt (eV) | 1.602 176 634 x 10-19 J | Exact since 2019 | Atomic and particle physics |
| 1 erg | 10-7 J | Exact | Astrophysics, CGS papers |
| 1 calorie (thermochemical) | 4.184 J | Exact | Calorimetry, chemistry |
| 1 food Calorie (kcal) | 4184 J | Exact | Nutrition labels |
| 1 foot pound-force (ft·lbf) | 1.355 82 J | Exact to more digits | US mechanical work |
| 1 BTU (international table) | 1055.055 852 62 J | Exact | Heating and cooling ratings |
| 1 kilowatt-hour (kWh) | 3.6 x 106 J | Exact | Electricity bills |
The electronvolt deserves a second look, because it is defined rather than measured. Since the 2019 redefinition fixed the elementary charge at exactly 1.602 176 634 x 10-19 C, the eV-to-joule factor is now exact by construction.
Going the other way, 1 J = 6.241 509 074 x 1018 eV. That vast ratio is precisely why nobody quotes a photon in joules — a visible photon carries a few eV, and writing it as 0.000 000 000 000 000 000 4 J helps no one. For the underlying concept, see our explainer on what energy is in physics.
One warning on calories. The “calorie” on a food label is a kilocalorie — 1000 thermochemical calories — so a 250 Calorie snack is 250 kcal, or roughly 1.05 x 106 J.
Pressure Conversions: Pa, kPa, atm, bar and psi
The pascal is one newton per square metre, which makes it a remarkably small unit. Atmospheric pressure is about 101 000 Pa, so real-world pressures almost always appear with a prefix or in a legacy unit.
| Unit | Value in pascals | Exact? | Where you meet it |
|---|---|---|---|
| 1 kilopascal (kPa) | 1000 Pa | Exact | Tyre placards, weather |
| 1 bar | 100 000 Pa | Exact | Meteorology, diving |
| 1 standard atmosphere (atm) | 101 325 Pa | Exact | Gas laws, chemistry |
| 1 torr | 133.322 Pa | Exactly 101 325/760 Pa | Vacuum systems |
| 1 mmHg (conventional) | 133.322 387 415 Pa | Exact | Blood pressure, barometry |
| 1 psi (lbf/in2) | 6894.76 Pa | Exact to more digits | Tyres, US engineering |
Note that 1 bar and 1 atm are close but not equal — 1 atm is 1.013 25 bar. Treating them as identical introduces a 1.3% error, which is fine for a rough estimate and fatal in a gas-law calculation.
Torr and mmHg are a second near-miss. Torr is defined as exactly one seven-hundred-and-sixtieth of an atmosphere, while the conventional millimetre of mercury is defined from a fixed mercury density — they agree to about one part in ten million. For the underlying physics, see our guide to pressure in physics.
Temperature Conversions: K, °C and °F, Where the Rule Changes
Temperature is the one place the conversion-ratio method fails, because the Celsius and Fahrenheit scales do not put zero at absolute zero. You must shift as well as scale.
- T — thermodynamic temperature, unit kelvin (K)
- t — Celsius or Fahrenheit temperature, unit degree Celsius (°C) or degree Fahrenheit (°F)
- 273.15 — the exact offset between the kelvin and Celsius scales
The 273.15 offset between kelvin and Celsius, and why Fahrenheit needs a factor as well as a shift.
| Reference point | Kelvin (K) | Celsius (°C) | Fahrenheit (°F) |
|---|---|---|---|
| Absolute zero | 0 | -273.15 | -459.67 |
| Water freezes | 273.15 | 0 | 32 |
| Room temperature | 293.15 | 20 | 68 |
| Body temperature | 310.15 | 37 | 98.6 |
| Water boils | 373.15 | 100 | 212 |
| An interval of 1 degree | 1 K | 1 °C | 1.8 °F |
Readings shift, but differences do not
Here is the subtlety that separates a confident answer from a lucky one. A reading of 25 °C converts to 298.15 K, but a rise of 25 °C is a rise of exactly 25 K — no offset at all.
The reason is that the offset cancels when you subtract two temperatures. So in any formula containing ΔT, such as Q = mcΔT, you may use Celsius and kelvin interchangeably. Our guide to heat versus temperature unpacks why that distinction matters physically.
Absolute temperatures are a different story. Anything with T alone — the ideal gas law, Stefan-Boltzmann, Carnot efficiency — needs kelvin, because a scale that can go negative would let you compute negative pressures and impossible efficiencies.
Common Misconceptions About Physics Unit Conversions
“You write degrees kelvin, °K”
No — the correct symbol is K, with no degree sign and no “degrees” in speech. The 13th General Conference on Weights and Measures dropped “degree Kelvin” in favour of the kelvin, as BIPM’s history of the kelvin records. It is 300 K, read aloud as “three hundred kelvin”.
“Converting kg to N is a unit conversion”
It is not. Kilograms measure mass and newtons measure force, so no conversion ratio connects them. Multiplying by g is a physics step that answers a different question — what does this mass weigh, here?
“Just use 273 instead of 273.15”
Rounding the offset costs you about 0.05%, which sounds harmless and quietly wrecks precision work. In a gas-law problem at 300 K, that is a 0.15 K error carried into every subsequent line — and it is free to avoid.
“A prefix on a squared unit still means the same power of ten”
The exponent applies to the whole unit, prefix included. So 1 m2 = 10 000 cm2, not 100 — and 1 m3 = 1 000 000 cm3. Sanity-check by asking whether the number moved in the direction you expected.
How Unit Conversions Relate to SI Units, Constants and Dimensional Analysis
Conversions sit on top of the SI system rather than beside it. Every derived unit decomposes into the seven base units, which is why a joule can be rewritten as kg·m2/s2 and a pascal as kg/(m·s2) — our guide to SI units in physics covers that structure in full.
That decomposition gives you a free check on any equation. If you reduce both sides to base units and they disagree, the equation is wrong — no arithmetic required. Dimensional analysis catches an inverted conversion ratio faster than re-checking the numbers ever will.
Constants tie the same knot. Many are quoted in more than one unit system, and picking the wrong one silently rescales your answer; our table of physics constants lists them with the units attached, which is the safest way to store them.
For exact factors beyond the ones tabulated here, NIST Special Publication 811, Appendix B is the reference to keep bookmarked. It marks which factors are exact by definition and which have been rounded.
Worked Problems
Show Solution
Solution:
Step 1: The prefix kilo means 103, so 1 kN = 1000 N. The conversion ratio is 1 kN / 1000 N.
Step 2: 24 500 N x (1 kN / 1000 N) = 24 500 / 1000 kN.
Step 3: The unit N cancels top and bottom, leaving kN.
Answer: 24.5 kN
Show Solution
Solution:
Step 1: Two ratios are needed, one for length and one for time: 1000 m / 1 km and 1 h / 3600 s.
Step 2: 108 km/h x (1000 m / 1 km) x (1 h / 3600 s) = (108 x 1000) / 3600 m/s.
Step 3: 108 000 / 3600 = 30. Both km and h cancel, leaving m/s.
Answer: 30.0 m/s
Show Solution
Solution:
Step 1: This is an absolute temperature, so use T(K) = t(°C) + 273.15.
Step 2: T = 27 + 273.15.
Step 3: T = 300.15 K. Note that no multiplication appears — the scales share a step size.
Answer: 300.15 K
Show Solution
Solution:
Step 1: Convert mass and volume separately: 1 kg / 1000 g, and 1 cm3 = 10-6 m3, so the volume ratio is 106 cm3 / 1 m3.
Step 2: 7.87 g/cm3 x (1 kg / 1000 g) x (106 cm3 / 1 m3) = 7.87 x 106 / 1000 kg/m3.
Step 3: 7.87 x 1000 = 7870. The cube on cm brought in 106, not 102.
Answer: 7870 kg/m3
Show Solution
Solution:
Step 1: Use the exact defined factor 1 eV = 1.602 176 634 x 10-19 J.
Step 2: E = 2.50 eV x (1.602 176 634 x 10-19 J / 1 eV).
Step 3: E = 4.005 441 585 x 10-19 J, rounded to the 3 significant figures of the input.
Answer: 4.01 x 10-19 J
Show Solution
Solution:
Step 1: By definition 1 atm = 101 325 Pa exactly.
Step 2: P = 2.50 atm x (101 325 Pa / 1 atm) = 253 312.5 Pa.
Step 3: Rounding to 3 significant figures gives 2.53 x 105 Pa, and dividing by 1000 gives kPa.
Answer: 2.53 x 105 Pa, or 253 kPa
Show Solution
Solution:
Step 1: A watt is a joule per second, so 1 kWh = 1000 W x 3600 s = 3.6 x 106 J.
Step 2: E = 2.4 kWh x (3.6 x 106 J / 1 kWh).
Step 3: E = 8.64 x 106 J.
Answer: 8.64 x 106 J (8.64 MJ)
Show Solution
Solution:
Step 1: Three ratios are needed: 4.184 J / 1 cal, 1000 g / 1 kg, and the interval identity 1 °C = 1 K.
Step 2: The °C here is a temperature difference, not a reading, so no 273.15 offset applies — the degree simply becomes a kelvin.
Step 3: 1.00 x (4.184 J / 1 cal) x (1000 g / 1 kg) = 4184 J/(kg·K).
Answer: 4184 J/(kg·K), or 4.18 x 103 J/(kg·K) to 3 significant figures
