A physical quantity is a property you can measure, and it always has two parts: a number and a unit. “5” tells you nothing. “5 m” is a length, “5 s” is a time, “5 kg” is a mass. Drop the unit and the number stops describing anything in the physical world.
That pairing is the whole idea. The rest of this post sorts physical quantities in the two ways physicists do it, and shows how every quantity you’ll meet is built from just seven.
Table of contents
- What counts as a physical quantity
- Scalar vs vector quantities
- Base vs derived quantities
- The seven SI base quantities
- Common derived quantities
- Quantity, unit and dimension are not the same thing
- Dimensional analysis in practice
- Common mistakes
- Practice questions
- Summary
What counts as a physical quantity
A physical quantity is anything you can measure and express as a magnitude (how much) multiplied by a unit (compared to what). The length of your desk is 1.4 m. The temperature of boiling water at sea level is 373.15 K. Both fit.
Things you can’t measure don’t qualify. “Beauty” has no unit. “Boredom” has no unit. “Speed” does, which is why it’s a physical quantity.
Written as an equation, a quantity is always number × unit. That’s why 1.4 m and 140 cm describe the same length: the number changes when the unit changes, but the quantity doesn’t.
Scalar vs vector quantities
The first way to classify physical quantities is by whether direction matters.
Scalar quantities have magnitude only. Common examples of scalar quantities include mass, time, temperature, energy and distance. “20 kg” is a complete statement.
Vector quantities have magnitude and direction. Force, velocity, acceleration, displacement and momentum are vectors. “20 N” is incomplete; “20 N downward” is not.
The cleanest way to feel the difference is to compare pairs that sound alike:
| Scalar | Vector | What separates them |
|---|---|---|
| Distance | Displacement | Distance is the length of the path you walked. Displacement is the straight-line change in position, with a direction. |
| Speed | Velocity | Speed is how fast. Velocity is how fast and which way. |
Run one full lap of a 400 m athletics track. Your distance is 400 m. Your displacement is zero, because you finished where you started. Your average speed is a positive number; your average velocity over that lap is zero too.
Direction also changes how you add quantities. Two masses of 3 kg and 4 kg always make 7 kg. Two forces of 3 N and 4 N can make anything from 1 N to 7 N, and exactly 5 N if they act at right angles. Scalars add like numbers. Vectors add like arrows.
Base vs derived quantities
The second classification is about construction. Some quantities are defined on their own. Others are built by combining those.
Base quantities are the independent building blocks. You can’t express length in terms of mass or time; each stands alone.
Derived quantities are combinations of base quantities, usually through multiplication and division. Speed is length divided by time. Area is length times length. Density is mass divided by volume, which is mass divided by length cubed.
Each derived quantity inherits a derived unit. Speed is measured in metres per second (m/s), which is just the base units of length and time written as a ratio. Nothing new is added.
The seven SI base quantities
The International System of Units (SI) picks seven base quantities. Everything else in physics and chemistry is derived from them. The International Bureau of Weights and Measures maintains the definitions.
| Base quantity | Typical symbol | SI unit | Unit symbol | Dimension symbol |
|---|---|---|---|---|
| Length | l, x | metre | m | L |
| Mass | m | kilogram | kg | M |
| Time | t | second | s | T |
| Electric current | I | ampere | A | I |
| Thermodynamic temperature | T | kelvin | K | Θ |
| Amount of substance | n | mole | mol | N |
| Luminous intensity | Iv | candela | cd | J |
Two oddities worth knowing. The kilogram is the only base unit with a prefix built in, so the gram is technically the awkward one. And “amount of substance” sounds vague but means something precise: it counts particles, with one mole being exactly 6.02214076 × 10²³ of them.
The SI units themselves changed in 2019. On 20 May 2019, all four of the remaining definitions that relied on physical objects or measurement conditions were replaced with definitions based on fixed constants of nature. The kilogram, for example, used to be the mass of a platinum-iridium cylinder kept in a vault near Paris. It’s now defined by fixing the Planck constant at exactly 6.62607015 × 10⁻³⁴ joule-seconds, as NIST explains. A cylinder can gather dust and lose atoms. A constant of nature can’t.
Common derived quantities
Here’s how the derived quantities most students meet first are assembled from the base ones.
| Derived quantity | Formula | SI unit | In base units |
|---|---|---|---|
| Area | length × length | m² | m² |
| Volume | length³ | m³ | m³ |
| Speed | distance ÷ time | m/s | m s⁻¹ |
| Acceleration | change in velocity ÷ time | m/s² | m s⁻² |
| Force | mass × acceleration | newton (N) | kg m s⁻² |
| Pressure | force ÷ area | pascal (Pa) | kg m⁻¹ s⁻² |
| Energy (work) | force × distance | joule (J) | kg m² s⁻² |
| Power | energy ÷ time | watt (W) | kg m² s⁻³ |
Read the last column and the pattern appears. A newton isn’t a separate unit of nature; it’s shorthand for “one kilogram-metre per second squared”. Special names like newton, joule and watt exist because writing kg m² s⁻³ every time would be miserable.
Quantity, unit and dimension are not the same thing
Three words get used interchangeably, and they shouldn’t be.
- A quantity is the property being measured: length, force, energy.
- A unit is the agreed amount you measure it against: metre, newton, joule.
- A dimension is the type of quantity, expressed in terms of the base quantities: L, MLT⁻², ML²T⁻².
Length is a quantity. The metre, the foot and the light-year are all units of it—detailed in our reference guide on units of measurement. Its dimension is L regardless of which unit you pick. This is why you can say a speed has dimensions L T⁻¹ without choosing between km/h and mph.
Dimensional analysis in practice
Dimensions give you a free error check. Every term in a valid equation must have the same dimensions, and you can only add or compare quantities that match.
Take kinetic energy, ½mv². Mass is M. Velocity squared is (L T⁻¹)² = L² T⁻². Multiply: M L² T⁻². That’s the dimension of energy, which matches the joule (kg m² s⁻²). The equation passes.
Now try a wrong one: suppose someone claims energy equals mv. That gives M L T⁻¹, which is momentum. Dimensions flag the mistake immediately, with no calculator involved.
The method has limits. It can’t catch a missing dimensionless number (the ½ above), and it can’t tell you whether a formula is true, only whether it’s consistent. But for a thirty-second sanity check, nothing is cheaper.
Ignoring units has real costs. In 1999 NASA’s Mars Climate Orbiter was lost because one team’s software produced thrust data in pound-force seconds while another team’s software expected newton seconds, per NASA’s mission records. A roughly $125 million spacecraft burned up in the Martian atmosphere over a unit mismatch.
Common mistakes
- Confusing mass and weight. Mass (kg) is how much matter an object has and stays the same everywhere. Weight is a force (N) from gravity. An astronaut’s mass is identical on the Moon; their weight drops to about a sixth.
- Treating a unit as a quantity. “The newton is a force” is loose. Force is the quantity; the newton is its unit.
- Using distance and displacement as synonyms. They only match for straight-line motion in one direction.
- Forgetting direction on vectors. A velocity of 30 m/s is a speed until you say which way.
- Mixing unit systems mid-calculation. Convert everything to SI first, then compute.
- Calling “temperature” in Celsius a base quantity unit. The SI base unit is the kelvin. Celsius is a derived scale offset by 273.15.
Practice questions
1. Is energy a scalar or a vector? Scalar. It has magnitude only.
2. A car drives 3 km east, then 4 km north. What’s the distance and the magnitude of the displacement? Distance is 7 km. Displacement is the hypotenuse of a 3-4-5 triangle: 5 km, pointing north of east.
3. Express the unit of pressure in SI base units. Pressure is force ÷ area. Force is kg m s⁻²; area is m². So pressure is kg m⁻¹ s⁻².
4. What are the dimensions of acceleration? Velocity per time: (L T⁻¹) ÷ T = L T⁻².
5. Is “speed = distance × time” dimensionally correct? No. Distance × time gives L T. Speed needs L T⁻¹.
Summary
Physical quantities are measurable properties written as a number times a unit. You can classify them by direction (scalar or vector) and by construction (base or derived). The SI system rests on seven base quantities: length, mass, time, electric current, temperature, amount of substance and luminous intensity. Everything else, from force to power, comes from combining them, and dimensions let you check that the combination makes sense.
Keep the three terms apart (quantity, unit, dimension) and most of the confusion in introductory physics goes away.
