Dimensions and Units
Every physical quantity has a unit; SI units form a common system.
About this topic
Every physical quantity has dimensions (length, mass, time) and is measured in units. The SI system has base units: metre, kilogram, second, ampere, kelvin, mole and candela, with others derived, such as the newton (kg·m/s²).
Prefixes like kilo-, milli- and micro- scale units by powers of ten: kilo is 1000, milli is one thousandth, and micro is one millionth. Checking that both sides of an equation have the same dimensions is a powerful way to catch mistakes, and it can even help you guess the form of a formula.
Example: in s = ut + ½at², each term has dimensions of length, since velocity times time and acceleration times time squared both reduce to metres. A formula such as s = ut + at would fail the check. In 1999 NASA lost the Mars Climate Orbiter after one team used pound-force seconds and another used newton seconds, a costly unit mix-up.
Tips: convert everything to SI before calculating, write units on every number, and use scientific notation for very large or small values. Be careful with area and volume conversions: 1 m² is 10,000 cm², not 100 cm².
Key ideas
- Base units: m, kg, s, A, K, mol, cd
- Convert with factors
- Check equations with units
Quick check
Use cases: where Dimensions and Units helps
- Homework: review the key idea behind Dimensions and Units before you start a problem set.
- Exam revision: use the quick check to test whether you can recall Dimensions and Units without notes.
- Visual learning: play with the interactive lab to see how Dimensions and Units changes when you adjust its inputs.
- Teaching a friend: explain Dimensions and Units in your own words, then compare your version with the key ideas.
The same laws describe car crashes, sports, satellites and everyday machines.
Frequently asked questions
What is Dimensions and Units?
Every physical quantity has a unit; SI units form a common system.
What will I learn in Dimensions and Units?
Base units: m, kg, s, A, K, mol, cd. Convert with factors. Check equations with units.
Is Dimensions and Units part of Physics?
Yes. It is one of 150 Physics topics on LearnViz HighSchoolEdu, with 3 key ideas, a live animation and a quick check.
Does the Dimensions and Units lab work on a phone or tablet?
Yes. The animation resizes to fit your screen and supports touch, so you can drag, tap and slide with your finger.
How should I study Dimensions and Units?
Read the summary and key ideas first, play with the interactive lab to see the idea in motion, then answer the quick check. If you get a question wrong, go back to the key idea it tests.
Do I need an account, and is my progress saved?
No account is needed. Marking a topic as learned is saved in your own browser, so it stays on that device and is not sent to a server.