Physics & Engineering Units: The Complete Guide
Engineers and scientists are surrounded by units that civilians rarely think about. Speed in knots. Pressure in pascals. Energy in joules, calories, kilowatt-hours, or BTUs depending on which industry you're in. Torque in newton-meters or pound-feet. Sound in decibels — a logarithmic scale that nobody finds intuitive on first encounter. And fuel efficiency in miles per gallon, liters per 100 kilometers, or kilometers per liter, with the second one being inverse in a way that breaks most people's mental math.
This pillar walks through the major derived physical units in the order an engineer is most likely to meet them in a working day. We'll cover the seven SI base units, the most useful derived units, and the cross-system conversions that turn an American spec sheet into a European one (or vice versa).
For instant conversion, the scientific converter handles speed, pressure, energy, power, and force in a single tabbed interface. Dedicated converters exist for the more specialized units.
The Seven SI Base Units
Every physical measurement in modern science reduces to combinations of these seven:
| Quantity | Unit | Symbol |
|---|---|---|
| Length | meter | m |
| Mass | kilogram | kg |
| Time | second | s |
| Electric current | ampere | A |
| Thermodynamic temperature | kelvin | K |
| Amount of substance | mole | mol |
| Luminous intensity | candela | cd |
Since the 2019 SI redefinition, all seven are tied to physical constants (the speed of light, Planck's constant, the elementary charge, etc.) rather than physical artifacts. The kilogram, for example, used to be defined by a literal cylinder of platinum-iridium in a French vault; it's now defined by Planck's constant.
Every other unit you'll meet — newton, joule, watt, pascal, hertz, volt, ohm — is a derived unit built from combinations of the base seven.
| Derived unit | Symbol | In base units |
|---|---|---|
| Newton (force) | N | kg·m/s² |
| Joule (energy) | J | kg·m²/s² |
| Watt (power) | W | kg·m²/s³ |
| Pascal (pressure) | Pa | kg/(m·s²) |
| Hertz (frequency) | Hz | 1/s |
| Volt (electric potential) | V | kg·m²/(s³·A) |
Speed and Velocity
Speed is the simplest derived unit: length divided by time. Common units:
| Unit | In m/s | Use |
|---|---|---|
| m/s | 1 | SI standard |
| km/h | 0.278 | Most road signs worldwide |
| mph | 0.447 | US/UK road speed |
| knot | 0.514 | Aviation and shipping |
| ft/s | 0.305 | US engineering |
| Mach (sea level) | ~343 | Aerospace |
A knot is one nautical mile per hour, where a nautical mile (1.852 km) corresponds to one minute of latitude on Earth's surface. That's why ship and plane speeds are reported in knots — they translate directly to "how many minutes of latitude do I cross per hour."
💡 Fun fact: The word "knot" comes from the log line — a rope thrown overboard with knots tied at fixed intervals. Sailors counted how many knots ran out in 30 seconds to estimate speed.
Pressure — Pa, bar, psi, atm
Pressure is force per area. The SI unit is the pascal (Pa = N/m²), but pascals are tiny — atmospheric pressure is about 101,325 Pa, which is why most working units are larger:
| Unit | In Pa | Used for |
|---|---|---|
| Pa | 1 | Scientific |
| hPa (millibar) | 100 | Weather forecasts (Europe) |
| kPa | 1,000 | Engineering |
| bar | 100,000 | European industry, tires (EU) |
| atm | 101,325 | Chemistry |
| psi | 6,895 | US engineering, tires (US) |
| Torr (mmHg) | 133.3 | Medicine, vacuum systems |
| inHg | 3,386 | US weather, aviation |
Blood pressure is uniquely reported in mmHg (millimeters of mercury) — a 120/80 reading means systolic pressure can support a column of mercury 120 mm tall.
Tire pressure in the US is in psi (~32–35 psi typical for cars); in Europe it's in bar (~2.2–2.4 bar) or sometimes kPa (~220–240 kPa). The pressure converter handles all of these in one place.
Energy — Joule, Calorie, kWh, BTU
Energy is the most over-unit-ed quantity in everyday life:
| Unit | In J | Use |
|---|---|---|
| J | 1 | SI |
| cal | 4.184 | Chemistry, nutrition (with "k") |
| kcal (Cal) | 4,184 | Food calories |
| Wh | 3,600 | Electronics |
| kWh | 3,600,000 | Electricity bills |
| BTU | 1,055 | US HVAC, gas appliances |
| eV | 1.602×10⁻¹⁹ | Particle physics |
| therm | 105,506,000 | US natural gas billing |
Your electricity bill is in kWh (kilowatt-hours): the energy delivered by 1 kilowatt of power for 1 hour. A typical US household uses about 900 kWh per month; a typical European one closer to 350 kWh.
Air conditioners are rated in BTU/hr in the US (a "12,000 BTU" window unit produces 3.5 kW of cooling). In Europe, they're rated directly in kW.
💡 Fun fact: The word "calorie" was coined in 1824 by French physicist Nicolas Clément. The capital-C "Calorie" used on US food labels is really a kilocalorie — 1,000 of the original tiny calories.
Power — Watt and Horsepower
Power is energy per unit time. The SI unit is the watt (W = J/s):
| Unit | In W |
|---|---|
| W | 1 |
| kW | 1,000 |
| MW | 1,000,000 |
| HP (mechanical) | 745.7 |
| HP (metric, PS) | 735.5 |
| BTU/hr | 0.293 |
| ft·lb/s | 1.356 |
Horsepower was defined in 1782 by James Watt to market his improved steam engines. He measured how much weight a draft horse could lift over a given time and rounded the figure. The "mechanical HP" used in the US (745.7 W) is slightly larger than the "metric HP" (PS, Pferdestärke) used in Europe (735.5 W). Most car manufacturers worldwide use kW as the primary spec, with HP as the marketing number.
For a deeper look, see Horsepower vs Kilowatts.
Force — Newton and Pound-Force
Force is mass times acceleration:
F = m × a
1 N = 1 kg × 1 m/s²
| Unit | In N |
|---|---|
| N | 1 |
| kN | 1,000 |
| lbf | 4.448 |
| kgf (kp) | 9.807 |
| dyne | 0.00001 |
A typical adult's weight on Earth is about 700 N (≈ 70 kg × 9.81 m/s² gravity). Rocket thrust is measured in kN or MN — the Saturn V's first stage produced 35 MN.
Torque — Twisting Force
Torque looks like energy (both are force × distance) but it isn't — it's the rotational analog of force. SI unit is the newton-meter (N·m), and US engineering uses pound-foot (lb·ft):
1 lb·ft = 1.356 N·m
1 N·m = 0.738 lb·ft
Most modern cars publish torque figures in both. A Honda Civic might produce 200 N·m / 148 lb·ft; a diesel pickup truck 1,000 N·m / 740 lb·ft.
The torque converter handles all the common pairs.
Frequency — Hertz and RPM
Frequency is cycles per unit time. The SI unit is the hertz (Hz = 1/s), named after Heinrich Hertz who demonstrated radio waves in 1887.
| Unit | In Hz |
|---|---|
| Hz | 1 |
| kHz | 1,000 |
| MHz | 1,000,000 |
| GHz | 10⁹ |
| RPM | 1/60 (= 0.0167) |
| BPM | 1/60 |
An engine idling at 800 RPM is running at 13.3 Hz. A 4 GHz CPU is doing 4 billion cycles per second. Wi-Fi 6 operates at 6 GHz. Human-audible sound is 20 Hz to 20 kHz.
The frequency converter covers Hz/RPM/BPM and the SI prefixes.
Sound and Decibels — The Logarithmic Trickster
Sound intensity is reported in decibels (dB), which is a logarithmic scale — and that's the part that confuses everyone.
dB = 10 × log10(I / I_reference)
Key implications:
- +3 dB doubles the intensity (not +100%).
- +10 dB is 10× the intensity and perceived as roughly twice as loud.
- +20 dB is 100× the intensity.
| Sound | dB SPL |
|---|---|
| Threshold of hearing | 0 |
| Whisper | 30 |
| Quiet office | 40 |
| Normal conversation | 60 |
| Vacuum cleaner | 70 |
| Heavy traffic | 85 |
| Power tools | 100 |
| Rock concert | 120 |
| Threshold of pain | 130 |
| Jet engine (close) | 140 |
Damage to hearing begins at sustained exposure above 85 dB. Brief exposure above 120 dB is immediately dangerous.
The sound converter handles dB, bel, and neper conversions for the rare cases that come up in engineering.
💡 Fun fact: The decibel is named after Alexander Graham Bell. The "bel" was the original unit but proved too coarse for practical work, so the deci-bel — one-tenth of a bel — became standard.
Electric Current — The Ampere
Current is the flow of electric charge, measured in amperes (A). Voltage (V) is the potential difference driving the current. The relationship, via Ohm's law:
V = I × R
Where R is resistance in ohms (Ω). Power, current, and voltage relate by:
P = V × I
A typical US household outlet delivers 120 V at up to 15 A — 1,800 W of available power. A typical EU outlet delivers 230 V at up to 16 A — 3,680 W. That's why European kettles boil water faster.
The electric converter handles unit prefixes (mA, μA, kA) and unit-of-charge conversions for batteries (Ah ↔ C).
Fuel Efficiency — The MPG/L per 100km Trap
Fuel efficiency is the most counter-intuitive unit in everyday use because L/100km is an inverse of MPG.
- MPG (miles per gallon): higher is better. Distance per fuel.
- km/L (kilometers per liter): higher is better. Distance per fuel.
- L/100km (liters per 100 km): lower is better. Fuel per distance.
A 30 MPG car (US) ≈ 7.84 L/100km ≈ 12.75 km/L A 40 MPG car (US) ≈ 5.88 L/100km ≈ 17.0 km/L
Doubling MPG (from 20 to 40) does NOT halve fuel use proportionally to the gap with a 50-MPG car. Improving from 20 to 25 MPG saves more fuel over 10,000 miles (100 gallons) than improving from 40 to 50 MPG (50 gallons). This is the MPG illusion — the linear-looking metric hides nonlinear savings.
Some conversions:
| US MPG | UK MPG | L/100km | km/L |
|---|---|---|---|
| 20 | 24 | 11.76 | 8.50 |
| 25 | 30 | 9.41 | 10.63 |
| 30 | 36 | 7.84 | 12.75 |
| 40 | 48 | 5.88 | 17.00 |
| 50 | 60 | 4.70 | 21.25 |
| 60 | 72 | 3.92 | 25.50 |
US gallons (3.785 L) differ from UK gallons (4.546 L), so UK MPG is always about 20% higher than US MPG for the same physical efficiency. The fuel converter handles the inversion safely.
Putting It All Together — Reading a Car Spec Sheet
A modern car spec sheet might say:
- 0–60 mph in 5.2 s
- 195 kW (262 HP) at 5,500 RPM
- 400 N·m (295 lb·ft) at 4,000 RPM
- 0.32 Cd (drag coefficient — dimensionless)
- 7.5 L/100km combined (31.4 US MPG)
- 35 psi tire pressure
- 12 V / 70 Ah battery
That single page touches half the units in this guide. The scientific converter handles speed/power/pressure/force/energy in one place; the dedicated torque, fuel, and electric converters handle the rest.
FAQ
Why is HP slightly different in different countries? Because James Watt's original definition (a horse lifting 33,000 ft·lb per minute) was approximate, and different countries rounded the SI equivalent differently. Mechanical HP (US) = 745.7 W; metric HP / PS (Europe) = 735.5 W. They differ by about 1.4%.
Why are decibels added rather than multiplied? Because the decibel is already a logarithm. Adding 10 dB to a 70 dB sound gives 80 dB — which is 10x the intensity. Logarithmic scales convert multiplications into additions.
Why does L/100km feel backwards to Americans? Because Americans think in "distance per fuel" (MPG), while Europeans think in "fuel per distance" (L/100km). Both work — the European metric is actually mathematically cleaner because cost and emissions scale linearly with it (twice the L/100km = twice the cost).
Are Pa really the SI pressure unit if no one uses them? Yes. Pascal is the official SI unit, but it's so small that everyone uses kilopascals, hectopascals (bar/100), or bar. The pascal is to pressure what the millimeter is to road distance — technically correct, practically inconvenient.
Why is the meter defined by the speed of light? Since 1983, the meter has been defined as the distance light travels in vacuum in 1/299,792,458 of a second. This locks the meter to a fundamental physical constant rather than a physical artifact, ensuring labs anywhere in the universe can reproduce it.
Related guides
- Blog: Horsepower vs Kilowatts — why power has so many units and which spec to trust.
- Converter: Scientific Converter — speed, pressure, energy, power, force tabs.
- Converter: Torque Converter — N·m, lb·ft, kgf·m and more.
- Converter: Frequency Converter — Hz, kHz, MHz, GHz, RPM.
- Converter: Sound Converter — dB, bel, neper.
- Converter: Electric Converter — amps, volts, ohms, watts.
- Converter: Fuel Efficiency Converter — MPG, L/100km, km/L without the inversion mistake.
- Quick conversions:
Physical units are the language engineers use to talk to each other across continents and centuries. Once you can speak it fluently, every spec sheet becomes readable.