Education Tools
Distance Between Points
Distance Between Points is part of Toolspire and is ready as soon as this page loads. Distance is the square root of (x2 − x1) squared plus (y2 − y1) squared. The units are whatever units the coordinates share.
On this page
What you can do here
A 3-4-5 check
The sample is the smallest integer Pythagorean triple, so a wrong square root is obvious.
Units are inherited
If both axes are in metres, the distance is in metres. The page does not convert.
Always non-negative
A distance does not carry a direction. Direction is the slope.
The sequence
How to use the Distance Between Points
- 1
Use the same unit on both axes
Mixing kilometres and metres makes a meaningless hypotenuse.
- 2
Confirm 5
(0, 0) to (3, 4) must read 5.
- 3
Open Pythagoras if you already have the two legs
This page computes the legs from coordinates first.
Worth knowing
- Distance Between Points on Toolspire: distance = √[(x2−x1)² + (y2−y1)²].
- (3, 4) from the origin is 5, because 9 + 16 = 25 and √25 = 5.
- The same point twice has distance 0.
- Slope is not the distance. The segment from (0, 0) to (2, 4) has slope 2 and length √20.
The coordinate form of Pythagoras
The horizontal gap and the vertical gap are the two legs of a right triangle. From the origin to (3, 4) those legs are 3 and 4, and the hypotenuse is 5. That is the distance formula, not a second theorem. Negative coordinates still square to a positive gap, so (−3, 0) to (0, 4) is the same length 5.
FAQ
Questions about Distance Between Points
Where does Distance Between Points run?
What is the distance from (0, 0) to (3, 4)?
What if the points are the same?
Does a negative coordinate make a negative distance?
Is distance the same as slope?
Keep going
Related tools
Last updated Report a problem or suggest a feature