Seven Units Build Every Measurement in Physics
Learn which physical quantities are fundamental and which are derived, the rules for writing SI symbols correctly, how to convert between SI, CGS and FPS and use prefixes, and how to derive the unit of any derived quantity.
Why do only seven quantities need their own units?
Physics measures hundreds of things — speed, force, pressure, energy, power, density. It might seem that each needs a unit of its own to be defined and remembered.
It does not. Speed is a length divided by a time, so its unit is and nothing new was needed. Force is a mass times an acceleration, so its unit is — again built from what was already there.
Keep going and almost everything collapses into combinations of a small handful of quantities. Exactly seven are chosen as the starting point, and the rest are built from them:
Those seven are the fundamental quantities, and everything else is derived.
The practical consequence is that a derived unit never has to be memorised. If you can write the defining formula, the unit follows from it in one line — and the last section of this page is nothing but that procedure applied five times.
This page covers the first part of the ICSE Class 9 Physics chapter on measurements and experimentation — the fundamental quantities, the conventions for writing units, conversions between systems, and deriving units.
It does not. Speed is a length divided by a time, so its unit is and nothing new was needed. Force is a mass times an acceleration, so its unit is — again built from what was already there.
Keep going and almost everything collapses into combinations of a small handful of quantities. Exactly seven are chosen as the starting point, and the rest are built from them:
Those seven are the fundamental quantities, and everything else is derived.
The practical consequence is that a derived unit never has to be memorised. If you can write the defining formula, the unit follows from it in one line — and the last section of this page is nothing but that procedure applied five times.
This page covers the first part of the ICSE Class 9 Physics chapter on measurements and experimentation — the fundamental quantities, the conventions for writing units, conversions between systems, and deriving units.
What are the seven fundamental quantities and their units?
They are the seven quantities the SI takes as given, each with one agreed unit and symbol.
- Length — metre, symbol
- Mass — kilogram, symbol
- Time — second, symbol
- Electric current — ampere, symbol
- Thermodynamic temperature — kelvin, symbol
- Amount of substance — mole, symbol
- Luminous intensity — candela, symbol
Derived quantities are those defined in terms of the seven, and their units follow:
- Area —
- Volume —
- Speed —
- Density —
- Force — , named the newton ()
- Pressure — , named the pascal ()
- Work and energy — , named the joule ()
- Power — , named the watt ()
- Momentum — , with no special name
Some derived units get their own name and some do not. The newton and the joule are named for convenience because they appear so often; momentum's unit is written out in full because nobody needed a shorthand. The naming is a convenience, not a promotion — a newton is still and can always be replaced by it.
Two quantities that measure similar things are kept separate. Mass is fundamental and measured in kilograms; weight is a force and measured in newtons. A kg bag of rice has a mass of kg everywhere, and its weight is about N on Earth and far less on the Moon. Everyday speech uses "weight" for mass, and physics does not.
"Fundamental" is a decision, not a discovery. Nothing in nature marks length as more basic than speed; a system could have been built taking speed and time as fundamental and deriving length from them. Seven was chosen because it is the smallest set that covers mechanics, electricity, heat, chemistry and light without overlap — and knowing that it is a convention makes the list easier to accept than trying to see why these seven are special.
- Length — metre, symbol
- Mass — kilogram, symbol
- Time — second, symbol
- Electric current — ampere, symbol
- Thermodynamic temperature — kelvin, symbol
- Amount of substance — mole, symbol
- Luminous intensity — candela, symbol
Derived quantities are those defined in terms of the seven, and their units follow:
- Area —
- Volume —
- Speed —
- Density —
- Force — , named the newton ()
- Pressure — , named the pascal ()
- Work and energy — , named the joule ()
- Power — , named the watt ()
- Momentum — , with no special name
Some derived units get their own name and some do not. The newton and the joule are named for convenience because they appear so often; momentum's unit is written out in full because nobody needed a shorthand. The naming is a convenience, not a promotion — a newton is still and can always be replaced by it.
Two quantities that measure similar things are kept separate. Mass is fundamental and measured in kilograms; weight is a force and measured in newtons. A kg bag of rice has a mass of kg everywhere, and its weight is about N on Earth and far less on the Moon. Everyday speech uses "weight" for mass, and physics does not.
"Fundamental" is a decision, not a discovery. Nothing in nature marks length as more basic than speed; a system could have been built taking speed and time as fundamental and deriving length from them. Seven was chosen because it is the smallest set that covers mechanics, electricity, heat, chemistry and light without overlap — and knowing that it is a convention makes the list easier to accept than trying to see why these seven are special.
How do you correct a wrongly written unit?
Apply the conventions one at a time: capitals only where required, no plurals, no full stops, a space before the symbol, and one solidus at most.
The rules.
- Unit names are lower case, even when named after a person: newton, joule, kelvin, pascal, ampere. The exception is degree Celsius
- Symbols from a person's name are capitalised: , , , , , . Others are lower case: , , , ,
- **Symbols take no plural **: , never
- No full stop after a symbol, except at the end of a sentence
- Leave a space between the number and the symbol: , not
- A prefix joins with no space: , ,
- Use at most one solidus. Write or , never
- Compound symbols take a space or a dot: or
Worked corrections.
- — capital wrong, plural wrong. Correct:
- — plural and full stop wrong, and the symbol is . Correct:
- — the symbol for metre is , not an abbreviation of the word. Correct:
- — as a name it should be lower case, 4 newtons; as a symbol,
- — two soliduses. Correct:
- — the kelvin takes no degree sign and its symbol is capital. Correct:
- — the prefix kilo is lower-case and metre is . Correct:
- — correct:
The capital matters because it changes the meaning. is metre and is the prefix mega; is kelvin and is kilo; is newton and is nano. So is a millinewton and is a megametre — a slip of case is a factor of a billion in some cases, which is why the rule is enforced rather than suggested.
Write the exponent form when in doubt. is unambiguous where invites a second slash later. For anything with two divisions — acceleration, density, pressure — the exponent form is the safer habit, and it is the form every derivation in the last section produces naturally.
The rules.
- Unit names are lower case, even when named after a person: newton, joule, kelvin, pascal, ampere. The exception is degree Celsius
- Symbols from a person's name are capitalised: , , , , , . Others are lower case: , , , ,
- **Symbols take no plural **: , never
- No full stop after a symbol, except at the end of a sentence
- Leave a space between the number and the symbol: , not
- A prefix joins with no space: , ,
- Use at most one solidus. Write or , never
- Compound symbols take a space or a dot: or
Worked corrections.
- — capital wrong, plural wrong. Correct:
- — plural and full stop wrong, and the symbol is . Correct:
- — the symbol for metre is , not an abbreviation of the word. Correct:
- — as a name it should be lower case, 4 newtons; as a symbol,
- — two soliduses. Correct:
- — the kelvin takes no degree sign and its symbol is capital. Correct:
- — the prefix kilo is lower-case and metre is . Correct:
- — correct:
The capital matters because it changes the meaning. is metre and is the prefix mega; is kelvin and is kilo; is newton and is nano. So is a millinewton and is a megametre — a slip of case is a factor of a billion in some cases, which is why the rule is enforced rather than suggested.
Write the exponent form when in doubt. is unambiguous where invites a second slash later. For anything with two divisions — acceleration, density, pressure — the exponent form is the safer habit, and it is the form every derivation in the last section produces naturally.
Formula
How do you convert between SI, CGS and FPS and use prefixes?
Replace each base unit by its equivalent, then multiply the conversion factors. A derived unit converts by the same powers that appear in its definition.
The three systems.
- SI: metre, kilogram, second
- CGS: centimetre, gram, second
- FPS: foot, pound, second
The key links are and .
Worked example 1 — the newton into the dyne. Force is , and the CGS unit is called the dyne:
Worked example 2 — the joule into the erg. Work is force times distance, so
Worked example 3 — density. Water has a density of . Converting: and , so
Note how the cube worked. The centimetre became a metre with a factor of , and **cubing it gave , not . A derived unit converts by the same power that appears in the unit, and forgetting to raise the factor is the commonest conversion error.
Worked example 4 — speed.** Convert into :
The factor is worth remembering, along with its reverse .
Worked example 5 — area. Convert into : , so and
The prefixes.
- micro, symbol —
- milli, symbol —
- kilo, symbol —
- mega, symbol —
Worked example 6 — using prefixes and standard form.
-
-
-
-
Standard form means one non-zero digit before the decimal point. Writing or gives the right value in the wrong format, and questions asking for standard form are testing the format as well as the arithmetic.
The three systems.
- SI: metre, kilogram, second
- CGS: centimetre, gram, second
- FPS: foot, pound, second
The key links are and .
Worked example 1 — the newton into the dyne. Force is , and the CGS unit is called the dyne:
Worked example 2 — the joule into the erg. Work is force times distance, so
Worked example 3 — density. Water has a density of . Converting: and , so
Note how the cube worked. The centimetre became a metre with a factor of , and **cubing it gave , not . A derived unit converts by the same power that appears in the unit, and forgetting to raise the factor is the commonest conversion error.
Worked example 4 — speed.** Convert into :
The factor is worth remembering, along with its reverse .
Worked example 5 — area. Convert into : , so and
The prefixes.
- micro, symbol —
- milli, symbol —
- kilo, symbol —
- mega, symbol —
Worked example 6 — using prefixes and standard form.
-
-
-
-
Standard form means one non-zero digit before the decimal point. Writing or gives the right value in the wrong format, and questions asking for standard form are testing the format as well as the arithmetic.
How do you derive the SI unit of force, density or pressure?
Write the defining formula, replace each quantity by its unit, and simplify. Nothing needs to be looked up.
Worked derivation 1 — force.
Mass is in and acceleration is a change of speed per time, so per , which is :
This combination is given the name newton (). So is the force that gives a mass of an acceleration of — a definition read straight off the unit.
Worked derivation 2 — density.
Worked derivation 3 — pressure.
Replacing the newton by its base units:
The name for this is the pascal ().
Worked derivation 4 — work and energy.
named the joule ().
Worked derivation 5 — power.
named the watt ().
Worked derivation 6 — momentum.
No special name, so it is written out.
Using units to check an equation. Since both sides of a physical equation measure the same thing, their units must match. Test :
- left side:
- right side:
They agree. Now test a wrong version, :
- right side:
That is the unit of momentum, not of work — so the equation is wrong, and the units said so without any need to recall the correct formula. This check catches a misremembered formula in one line, and it works on every equation you will meet.
Matching units does not guarantee a correct formula, though. Both and have the units of work, so a wrong numerical factor passes the test unnoticed. The check rules formulas out, never in — which is exactly the asymmetry the algebra chapter met when verifying identities by substitution.
Worked derivation 1 — force.
Mass is in and acceleration is a change of speed per time, so per , which is :
This combination is given the name newton (). So is the force that gives a mass of an acceleration of — a definition read straight off the unit.
Worked derivation 2 — density.
Worked derivation 3 — pressure.
Replacing the newton by its base units:
The name for this is the pascal ().
Worked derivation 4 — work and energy.
named the joule ().
Worked derivation 5 — power.
named the watt ().
Worked derivation 6 — momentum.
No special name, so it is written out.
Using units to check an equation. Since both sides of a physical equation measure the same thing, their units must match. Test :
- left side:
- right side:
They agree. Now test a wrong version, :
- right side:
That is the unit of momentum, not of work — so the equation is wrong, and the units said so without any need to recall the correct formula. This check catches a misremembered formula in one line, and it works on every equation you will meet.
Matching units does not guarantee a correct formula, though. Both and have the units of work, so a wrong numerical factor passes the test unnoticed. The check rules formulas out, never in — which is exactly the asymmetry the algebra chapter met when verifying identities by substitution.
Exam tip
Exam tip: state the unit with every answer and mind the case
Never write a bare number. A physics answer without its unit is incomplete and loses marks even when the arithmetic is right.
Case changes the meaning: is metre and is mega; is kilo and is kelvin; is nano and is newton.
Unit NAMES are lower case (newton, joule, pascal); SYMBOLS from a person's name are capital (, , ).
No plurals and no full stops on symbols: , not or
Leave a space before the symbol () but none after a prefix ().
Use at most one solidus — write , never . The exponent form is safer for anything with two divisions.
The kelvin takes no degree sign: , not .
When converting a squared or cubed unit, raise the factor too: , not .
Learn two conversions cold: , , and the speed factor for into .
Standard form has one non-zero digit before the point: , not .
To derive a unit, write the formula and substitute units — never memorise a derived unit.
And mass is in kilograms, weight is in newtons — a bag weighs about on Earth.
Case changes the meaning: is metre and is mega; is kilo and is kelvin; is nano and is newton.
Unit NAMES are lower case (newton, joule, pascal); SYMBOLS from a person's name are capital (, , ).
No plurals and no full stops on symbols: , not or
Leave a space before the symbol () but none after a prefix ().
Use at most one solidus — write , never . The exponent form is safer for anything with two divisions.
The kelvin takes no degree sign: , not .
When converting a squared or cubed unit, raise the factor too: , not .
Learn two conversions cold: , , and the speed factor for into .
Standard form has one non-zero digit before the point: , not .
To derive a unit, write the formula and substitute units — never memorise a derived unit.
And mass is in kilograms, weight is in newtons — a bag weighs about on Earth.
Did you know
Why a unit check can prove a formula wrong but never prove it right
Suppose you half-remember a formula for the time period of a pendulum and write down instead of .
Test the units. Length is in and is in , so
That is a speed, not a time. The formula is wrong, and you knew it in two lines without remembering anything.
Now try the correct version:
A time, as required. The check passed.
But passing proves less than it seems. The expression also has units of seconds, and so does with no factor at all. A unit check cannot see a pure number, because a pure number has no units to contribute — so any wrong constant slips through untouched.
The same blindness covers other things. It cannot tell from , since both are pure numbers, and it cannot tell a plus from a minus.
So the check has a precise power: it rules formulas out reliably and rules them in never. That is still worth a great deal in an exam, where the usual failure is writing instead of — a mistake units catch immediately.
It is the same shape of argument as testing an algebraic identity by substituting numbers. One failed substitution refutes the identity for good; a thousand successful ones prove nothing, because the next value might break it. Cheap tests that can only say no are worth running anyway, precisely because they are cheap.
Test the units. Length is in and is in , so
That is a speed, not a time. The formula is wrong, and you knew it in two lines without remembering anything.
Now try the correct version:
A time, as required. The check passed.
But passing proves less than it seems. The expression also has units of seconds, and so does with no factor at all. A unit check cannot see a pure number, because a pure number has no units to contribute — so any wrong constant slips through untouched.
The same blindness covers other things. It cannot tell from , since both are pure numbers, and it cannot tell a plus from a minus.
So the check has a precise power: it rules formulas out reliably and rules them in never. That is still worth a great deal in an exam, where the usual failure is writing instead of — a mistake units catch immediately.
It is the same shape of argument as testing an algebraic identity by substituting numbers. One failed substitution refutes the identity for good; a thousand successful ones prove nothing, because the next value might break it. Cheap tests that can only say no are worth running anyway, precisely because they are cheap.
Exam relevance
How do units and measurement feed into JEE Main and NEET?
Because unit analysis is a tool used in every numerical question, and the dimensional method it grows into is a chapter examined in its own right.
This is the foundation for Class 11 Physics Units and Measurements, examined in JEE Main and NEET. The derivation procedure on this page — write the formula, substitute units, simplify — becomes dimensional analysis, where units are replaced by the dimensional symbols , and . Force becomes , pressure , and work — the same expressions with letters in place of kilograms and metres.
Three standard uses of that method are examined directly. Checking whether an equation is dimensionally correct — exactly the pendulum test in the previous section. Converting a quantity between systems, which is worked example 1 and 2 of this page generalised. And deducing a formula up to a constant, where the units fix which powers of mass, length and time can appear. The limitation flagged here — that a pure numerical factor is invisible — is why the third use always ends with "up to a constant", and assertion-reason questions exploit precisely that.
Significant figures and error analysis join the chapter in Class 11, and the unit-writing conventions established here are enforced there too.
Where the base units matter in other chapters. Class 11 Thermodynamics uses the kelvin as the only temperature scale in which gas laws take their simple form; Class 11 Chemistry Some Basic Concepts uses the mole constantly; Class 12 Current Electricity uses the ampere. Each of the seven appears somewhere, which is why the list is worth learning as a list.
The mass-and-weight distinction is tested repeatedly. Questions on a body taken to the Moon or into orbit turn on mass staying the same while weight changes, and both JEE Main and NEET use it in Gravitation.
What the questions look like. For board work, expect state the fundamental quantities with units and symbols, correct wrongly written units, convert between systems or express with a prefix in standard form, and derive the SI unit of a given quantity from its formula. For JEE Main and NEET, expect dimensional-correctness checks, conversions of a numerical value between systems, and deducing the dependence of a quantity on others.
How board and competitive emphasis differ. A board paper rewards the stated conventions and the derivation written out line by line. A competitive paper assumes all of it and uses a dimensional check as a fast way to eliminate wrong options — often the quickest route to an answer when four formulas are offered and only one has the right dimensions.
The single trap that costs the most marks. Forgetting to raise the conversion factor when the unit carries a power. Going from to is a factor of , not , and the density conversion depends on getting it right. The defence is to convert the base unit first and then apply the power visibly, writing rather than jumping to a number.
This is the foundation for Class 11 Physics Units and Measurements, examined in JEE Main and NEET. The derivation procedure on this page — write the formula, substitute units, simplify — becomes dimensional analysis, where units are replaced by the dimensional symbols , and . Force becomes , pressure , and work — the same expressions with letters in place of kilograms and metres.
Three standard uses of that method are examined directly. Checking whether an equation is dimensionally correct — exactly the pendulum test in the previous section. Converting a quantity between systems, which is worked example 1 and 2 of this page generalised. And deducing a formula up to a constant, where the units fix which powers of mass, length and time can appear. The limitation flagged here — that a pure numerical factor is invisible — is why the third use always ends with "up to a constant", and assertion-reason questions exploit precisely that.
Significant figures and error analysis join the chapter in Class 11, and the unit-writing conventions established here are enforced there too.
Where the base units matter in other chapters. Class 11 Thermodynamics uses the kelvin as the only temperature scale in which gas laws take their simple form; Class 11 Chemistry Some Basic Concepts uses the mole constantly; Class 12 Current Electricity uses the ampere. Each of the seven appears somewhere, which is why the list is worth learning as a list.
The mass-and-weight distinction is tested repeatedly. Questions on a body taken to the Moon or into orbit turn on mass staying the same while weight changes, and both JEE Main and NEET use it in Gravitation.
What the questions look like. For board work, expect state the fundamental quantities with units and symbols, correct wrongly written units, convert between systems or express with a prefix in standard form, and derive the SI unit of a given quantity from its formula. For JEE Main and NEET, expect dimensional-correctness checks, conversions of a numerical value between systems, and deducing the dependence of a quantity on others.
How board and competitive emphasis differ. A board paper rewards the stated conventions and the derivation written out line by line. A competitive paper assumes all of it and uses a dimensional check as a fast way to eliminate wrong options — often the quickest route to an answer when four formulas are offered and only one has the right dimensions.
The single trap that costs the most marks. Forgetting to raise the conversion factor when the unit carries a power. Going from to is a factor of , not , and the density conversion depends on getting it right. The defence is to convert the base unit first and then apply the power visibly, writing rather than jumping to a number.
Key takeaways
Fundamental quantities, unit conventions and conversions: quick revision
- Seven fundamental quantities: length (metre, ), mass (kilogram, ), time (second, ), electric current (ampere, ), thermodynamic temperature (kelvin, ), amount of substance (mole, ), luminous intensity (candela, ).
- Derived quantities are built from those: area , volume , speed , density , momentum .
- Named derived units: newton ; pascal ; joule ; watt . Momentum has no special name.
- "Fundamental" is a convention, chosen as the smallest set covering every branch of physics.
- Mass is in kilograms; weight is a force in newtons. A bag weighs about on Earth.
- Unit NAMES are lower case (newton, joule); symbols from a person's name are capital (, , , , , ).
- **No plural , no full stop, a space before the symbol, none after a prefix, and at most one solidus.
- Corrections**: ; ; ; ; ; .
- Case changes the meaning: metre against mega, kilo against kelvin, nano against newton.
- Systems: SI (m, kg, s), CGS (cm, g, s), FPS (foot, pound, second).
- ****, since ; **.
- ** — note , cubed, not .
- **** using the factor ; .
- Prefixes: micro is , milli is , kilo is , mega is .
- ; ; ; .
- Standard form has one non-zero digit before the point.
- To derive a unit, substitute units into the formula: force ; pressure ; work ; power .
- A unit check refutes a wrong formula: gives , the unit of momentum, not of work.
- But it can never confirm one — a pure numerical factor has no units and passes unseen.
Pick five quantities from your physics book, cover their units, and derive each one from its formula — then check how many you would otherwise have had to memorise.
- Derived quantities are built from those: area , volume , speed , density , momentum .
- Named derived units: newton ; pascal ; joule ; watt . Momentum has no special name.
- "Fundamental" is a convention, chosen as the smallest set covering every branch of physics.
- Mass is in kilograms; weight is a force in newtons. A bag weighs about on Earth.
- Unit NAMES are lower case (newton, joule); symbols from a person's name are capital (, , , , , ).
- **No plural , no full stop, a space before the symbol, none after a prefix, and at most one solidus.
- Corrections**: ; ; ; ; ; .
- Case changes the meaning: metre against mega, kilo against kelvin, nano against newton.
- Systems: SI (m, kg, s), CGS (cm, g, s), FPS (foot, pound, second).
- ****, since ; **.
- ** — note , cubed, not .
- **** using the factor ; .
- Prefixes: micro is , milli is , kilo is , mega is .
- ; ; ; .
- Standard form has one non-zero digit before the point.
- To derive a unit, substitute units into the formula: force ; pressure ; work ; power .
- A unit check refutes a wrong formula: gives , the unit of momentum, not of work.
- But it can never confirm one — a pure numerical factor has no units and passes unseen.
Pick five quantities from your physics book, cover their units, and derive each one from its formula — then check how many you would otherwise have had to memorise.