Absolute Value
Absolute value measures distance from zero, so it is never negative.
About this topic
The absolute value of a number is its distance from zero on the number line, ignoring direction. It is written with vertical bars around the number, so the absolute value of −5 is 5 and the absolute value of 5 is also 5. Distance can never be negative, so absolute value is always zero or positive.
The idea extends to distance between two numbers: the distance from a to b is the absolute value of a − b. So the distance from −2 to 7 is the absolute value of −2 − 7, which is 9. Absolute value also shows up in measuring error, where you care how far off an estimate is rather than whether it is too high or too low.
Consider a submarine at −40 metres and a bird at 25 metres relative to sea level. Their distances from the surface are 40 and 25, and the distance between them is 65. A weather report might say a temperature is within 3 degrees of 20, which is written as the absolute value of T − 20 being at most 3.
Absolute value is also the foundation for absolute value equations, inequalities and for the size of vectors and complex numbers later on. A common misconception is that absolute value just removes the minus sign anywhere in an expression. It only applies to the whole quantity inside the bars: the absolute value of 3 − 8 is 5, not 3 + 8.
Key ideas
- ∣−5∣ = 5 and ∣5∣ = 5
- It strips the sign of a number
- The graph of ∣x∣ is a V shape
Quick check
Use cases: where Absolute Value helps
- Homework: review the key idea behind Absolute Value before you start a problem set.
- Exam revision: use the quick check to test whether you can recall Absolute Value without notes.
- Visual learning: play with the interactive lab to see how Absolute Value changes when you adjust its inputs.
- Teaching a friend: explain Absolute Value in your own words, then compare your version with the key ideas.
Number and algebra skills are used in science, engineering, budgeting and computing.
Frequently asked questions
What is Absolute Value?
Absolute value measures distance from zero, so it is never negative.
What will I learn in Absolute Value?
∣−5∣ = 5 and ∣5∣ = 5. It strips the sign of a number. The graph of ∣x∣ is a V shape.
Is Absolute Value part of Mathematics?
Yes. It is one of 200 Mathematics topics on LearnViz HighSchoolEdu, with 3 key ideas, a live animation and a quick check.
Does the Absolute Value 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 Absolute Value?
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.