Distance Calculator · Practical guide
Distance Between Two Points with Negative Coordinates
Negative coordinates change nothing — the subtraction can be negative, but the square is always positive.
At a glance
The Formula Handles Signs for You
Negative coordinates trip up more students than any other part of the distance formula, yet they require zero special handling. The difference between two coordinates can be negative, but squaring makes every term positive, so the same formula works whether your points sit in one quadrant or four.
Interactive tool
Distance Calculator
Enter your own values, then compare the result with the examples below.
Results
Worked Example Across Quadrants
Find the distance from (−2, 3) to (4, −5) — one point in quadrant II, the other in quadrant IV. Differences: 4 − (−2) = 6 and −5 − 3 = −8. Squared: 36 and 64. Sum: 100. Distance: d = 10. The midpoint is ((−2+4)/2, (3+(−5))/2) = (1, −1), down in quadrant IV.
The Mistake That Costs Points
Subtracting a negative must become addition. From (−2, 3) to (4, −5), the x-difference is 4 − (−2) = 4 + 2 = 6 — not 4 − 2 = 2. Write the double negative out explicitly before you compute, or enter the coordinates in the calculator above, which handles signs automatically.
Quick Check Set
| Point 1 | Point 2 | Distance |
|---|---|---|
| (−3, 0) | (3, 0) | 6 |
| (0, −4) | (0, 4) | 8 |
| (−1, −1) | (2, 3) | 5 |
| (−6, −8) | (0, 0) | 10 |
Each of these spans an axis or the origin — and every one resolves to a clean integer once the double negatives are handled correctly.
Frequently Asked Questions
Can a distance be negative?
Never. The formula squares each coordinate difference, so every term under the square root is positive or zero. Distance is zero only when the two points are identical.
How do I subtract a negative coordinate?
Turn it into addition: 4 − (−2) = 4 + 2 = 6. This is the single most common error in distance problems, so write the subtraction out longhand before squaring.
Does the midpoint formula work with negative coordinates?
Yes, just average the coordinates normally, keeping the signs: the midpoint of (−2, 3) and (4, −5) is (1, −1). Averages of opposite-sign numbers can be negative, positive, or zero.
Which quadrant is a point with both coordinates negative?
Quadrant III, down and to the left of the origin. Quadrants run counterclockwise: I (+,+), II (−,+), III (−,−), IV (+,−).