SPI Physics · Formula sheet
Units, Measurement and Dimensions formulas
1 formula, 4 reference tables and 12 common traps for SPI Physics Units, Measurement and Dimensions, grouped by subtopic.
Standard Units and Time
Learn this subtopic in the notesWhy we need standard units
| Old unit | Measured with |
|---|---|
| Angul | The width of a finger |
| Mutthi | A closed fist |
| Handspan (balisht) | The stretch from thumb tip to little finger tip |
| Cubit | The length from the elbow to the tip of the fingers |
| Foot | The length of a person's foot |
| Pace | The length of one step |
Ancient India measured small lengths in anguls and mutthis; the cubit was for longer lengths such as cloth.
Instants, intervals and units of time
| Unit | Equal to |
|---|---|
| Minute | 60 seconds |
| Hour | 60 minutes, or 3600 seconds |
| Day | 24 hours, or 86400 seconds |
| Year | 365 days (a leap year has 366) |
| Decade | 10 years |
| Century | 100 years |
| Millennium | 1000 years Ten centuries make a millennium. |
A trillion is a number (a million million), not a unit of time.
Common traps
Giving a use as the purpose
Buying, selling and keeping records all use standard units, but the reason a standard exists is uniformity: the same measurement for the same quantity everywhere.
Calling the yard an ancient Indian unit
The yard and the foot are British units and the metre is modern. Ancient India measured small lengths with the angul and the mutthi.
Calling a moment an interval
The time of sunrise, or 'at 5 o'clock', is an instant. An interval always lasts for some time, like a minute or a day.
Mixing up century and millennium
A century is 100 years and a millennium is 1000 years. A decade is 10 years.
Taking a trillion for a span of time
A trillion is a number, a million million. It is not a unit of time, so it cannot name 1000 years.
SI Units, Prefixes and Conversions
Learn this subtopic in the notesConverting CGS units to SI
CGS and SI
SI base units and derived units
| Quantity | SI unit | Symbol and meaning |
|---|---|---|
| Length | metre | m |
| Mass | kilogram | kg |
| Time | second | s |
| Electric current | ampere | A |
| Temperature | kelvin | K |
| Amount of substance | mole | mol |
| Luminous intensity | candela | cd |
| Force | newton | N, which is kg m/s² |
| Work and energy | joule | J, which is N m |
| Power | watt | W, which is J/s |
| Frequency | hertz | Hz, which is per second (s⁻¹) Per second, not second and not second squared. |
| Pressure | pascal | Pa, which is N/m² |
The first seven rows are the base units; the rest are derived from them.
Prefixes: powers of ten
| Prefix | Symbol | Value |
|---|---|---|
| giga | G | |
| mega | M | |
| kilo | k | |
| centi | c | |
| milli | m | |
| micro | μ | Micro is a thousand times smaller than milli. |
| nano | n |
Each step from kilo down to nano (missing out centi) is a factor of 1000.
Common traps
The gram as the SI unit of mass
The SI unit of mass is the kilogram. The gram is one thousandth of it and belongs to the CGS system.
Celsius as the SI unit of temperature
The SI base unit of temperature is the kelvin. The degree Celsius is in daily use, but it is not the SI unit.
Swapping milli and micro
Milli is and micro is . A microampere is a thousandth of a milliampere.
Reading capital M as milli
Capital M is mega (); small m is milli (). 1 MW is a million watts, not a thousandth of a watt.
Converting an area with the length factor
1 m is 100 cm, but 1 m² is cm², not 100 cm².
Getting the direction backwards
The SI unit is the bigger one: one newton is dynes, so a dyne is N, not N.
Mixing up dyne and erg
The dyne is the CGS unit of force and the erg is the CGS unit of energy. They pair with the newton and the joule.