Distance Between 3 Points Calculator
Three points on a plane hold more information than any single pair of them. Measure all three gaps between them and you know the sides of the triangle they form, whether they actually form one at all, and whether one of its corners is a perfect right angle.
This calculator takes the x and y coordinates of three points, A, B, and C, and returns the three pairwise distances, AB, BC, and CA, each to four decimal places. It is a 2D tool only: there are no z coordinates and no latitude and longitude here, just flat coordinate geometry done exactly.
2D points only, in any consistent unit: if your coordinates are in meters, the distances are in meters. This tool returns the three side lengths and does not add a perimeter total for you; the perimeter section below shows the one addition involved.
Quick Answer
Key takeaways
- One formula does all the work: the Euclidean distance between two points, run three times, once per pair.
- The three outputs are the sides of a triangle, so comparing them tells you the triangle type: all equal, two equal, all different, or right angled.
- If the longest distance equals the sum of the other two, the points are collinear and no triangle exists. The verdict badge under the results checks this for you.
- The tool returns the three sides only. A perimeter is one addition away (3.0000 + 4.0000 + 5.0000 = 12), and the sides also feed Heron's formula for area.
- Quick Answer
- How to use this calculator
- One formula, three pairs of points
- Worked example: the 3-4-5 triangle
- What the three sides tell you about the triangle
- Perimeter, area, and centroid from the same three sides
- What competing calculators miss
- Three points, two points, or a line: picking the right tool
- Frequently Asked Questions
- Add This Calculator to Your Website
How to use this calculator
Six fields, one click. The order of the points does not change the three distances, but it does name them, so keep track of which point is which.
Enter point A. Type its x and y coordinates into the first two fields. The pre-filled example starts A at the origin, (0, 0).
Enter points B and C. Same pattern: an x field and a y field each. Decimals and negative coordinates are accepted in all six fields.
Click Calculate. The results box appears with AB, BC, and CA to four decimal places, plus a verdict badge that classifies the triangle the three sides form.
Copy or share if you need the numbers elsewhere. The copy button packages the three points, the three distances, and the verdict into plain text. Reset restores the worked example and hides the results again.
One formula, three pairs of points
Every side comes from the same Euclidean distance formula, which is the Pythagorean theorem wearing coordinate clothes. The horizontal gap and the vertical gap between two points are the short sides of a right triangle, and the distance you want is its hypotenuse.
This is the same calculation that sits inside a rectangle's diagonal, which is why the diagonal distance calculator and this tool agree wherever they overlap: a diagonal is just the distance between opposite corners. What this page adds is repetition with bookkeeping. Running the formula three times by hand invites the classic slip of pairing the wrong coordinates, and the tool's whole job is to keep the pairs straight: A with B, B with C, C back to A.
Under the hood the tool uses JavaScript's Math.hypot function, which computes the same square root of squared sums with extra care against overflow on very large coordinates. The displayed value is that result rounded to four decimal places.
Worked example: the 3-4-5 triangle
The calculator is pre-filled with A (0, 0), B (3, 0), and C (3, 4). Here is each side worked by hand, exactly as the tool computes it.
| Side | Coordinate differences | Squares | Distance |
|---|---|---|---|
| AB | dx = 3 − 0 = 3, dy = 0 − 0 = 0 | 9 + 0 = 9 | 3.0000 |
| BC | dx = 3 − 3 = 0, dy = 4 − 0 = 4 | 0 + 16 = 16 | 4.0000 |
| CA | dx = 0 − 3 = −3, dy = 0 − 4 = −4 | 9 + 16 = 25 | 5.0000 |
The right angle sits at B, the corner where the two shorter sides meet. You can spot the pattern before any angle work: when the longest side squared equals the sum of the squares of the other two, the triangle is right angled, by the converse of the Pythagorean theorem. The verdict badge under the results runs that check on every calculation, not just this tidy one.
What the three sides tell you about the triangle
Three side lengths classify a triangle completely, and every test below runs on numbers this calculator has already produced for other point sets, so you can reproduce each row yourself.
| Test on AB, BC, CA | Verdict | Verified example |
|---|---|---|
| All three equal | Equilateral | Impossible with all whole-number coordinates; A (0, 0), B (4, 0), C (2, 3.4641) gives 4.0000, 4.0000, 4.0000 |
| Exactly two equal | Isosceles | A (0, 0), B (3, 4), C (6, 0) gives 5.0000, 5.0000, 6.0000 |
| All three different | Scalene | A (1, 2), B (4, 6), C (7, 3) gives 5.0000, 4.2426, 6.0828 |
| Longest² = sum of the other two squared | Right angled | The pre-filled 3.0000, 4.0000, 5.0000 example |
| Longest = sum of the other two | Collinear, no triangle | A (0, 0), B (1, 1), C (2, 2) gives 1.4142, 1.4142, 2.8284 |
| One side is 0 | Two points are identical | Enter the same coordinates for any two points |
The collinear row deserves a second look, because it catches people out in survey and mapping work. Points that look like a shallow triangle on a sketch can be exactly on one line, and the distance test is the reliable way to know: 1.4142 + 1.4142 = 2.8284, to the fourth decimal, so B sits exactly on the segment from A to C. This is the triangle inequality running in reverse. A genuine triangle needs the longest side strictly shorter than the other two added together.
Negative coordinates change nothing. A (−2, −3), B (4, −3), and C (4, 5) return 6.0000, 8.0000, and 10.0000, a 3-4-5 triangle scaled by two and shifted into the negative quadrant. The squaring step is what makes the signs irrelevant.
Perimeter, area, and centroid from the same three sides
The tool stops at the three sides, honestly and deliberately: those are the measurements. Three standard follow-on quantities start from them, and each takes one short hand calculation.
Perimeter is the sum of the sides: AB + BC + CA. For the worked example, 3.0000 + 4.0000 + 5.0000 = 12. If you are fencing a triangular plot or edging a triangular bed, the three sides plus this addition are the whole job.
Area comes from Heron's formula once the sides are known. Take half the perimeter, s = 6 for the worked example, then area = √[s(s − AB)(s − BC)(s − CA)] = √[6 × 3 × 2 × 1] = √36 = 6. That matches the direct right-triangle method, (3 × 4) / 2 = 6, which is a good cross-check whenever one corner is a right angle.
Centroid, the triangle's balance point, comes from the coordinates rather than the sides: average the three x values and the three y values. For the worked example, ((0 + 3 + 3) / 3, (0 + 0 + 4) / 3) = (2, 1.3333). The same averaging idea, weighted by mass instead of counted equally, is what the center of mass calculator for XY coordinates does for point masses on a plane.
What competing calculators miss
The two tools that rank for this exact term, at Brave Calculator and Savvy Calculator, both compute the same three sides and both add a perimeter total, which this tool does not print for you. That is their one genuine edge, and the perimeter section above covers the single addition it takes to match it. On everything else, their pages stop early.
Two decimal places instead of four. Brave Calculator states its results are shown with two decimal precision. Two decimals hide exactly the patterns this kind of problem is about: the collinear test above needs 1.4142 and 2.8284 at four places before the equality is convincing, and near-equal sides in a decimal problem get rounded into looking equal when they are not.
No triangle classification. Both competitors hand back three numbers and leave the interpretation to you. Neither flags a right angle, an isosceles pair, or the collinear trap. The verdict badge here runs the equality, Pythagorean, and collinearity checks on your actual numbers the moment you calculate.
No copy or share, and no worked steps. Their examples are static text with different numbers from yours. Here, the worked example is the pre-filled case in the calculator itself, so the hand calculation in the table above can be checked against the tool in one click, and the results travel with the copy and share buttons.
One honest limit in the other direction: this is a flat-plane tool. If your three points are GPS coordinates spread over kilometers, straight-line coordinate math on degrees will mislead you, because longitude degrees shrink toward the poles. That job belongs to a great-circle tool, not this one.
Three points, two points, or a line: picking the right tool
Stay on this page when you have exactly three 2D points and need every gap between them: triangle sides, plot corners, three survey markers, three vertices in a graphics problem.
Switch to the general distance calculator when you have one pair of points, especially if the pair lives in 3D space or is given as latitude and longitude. It returns the single distance with slope, midpoint, and step-by-step work for point pairs, and great-circle distance with bearing for GPS coordinates.
And when the question changes from "how far apart are these points" to "how far is this point from the line through the other two", that is a different measurement with its own tool: the distance from a point to a line calculator takes the same three points and returns the perpendicular distance instead of the three sides.
Frequently Asked Questions
It takes the coordinates of three points, A, B, and C, on a flat 2D plane and returns the three straight-line distances between them: AB, BC, and CA. Each distance is worked out with the Euclidean distance formula and shown to four decimal places. Those three numbers are the three sides of the triangle the points form, unless the points sit on one straight line.
No. The tool returns the three side lengths only, and the perimeter is the sum of the three: add AB, BC, and CA. For the pre-filled example that is 3.0000 + 4.0000 + 5.0000 = 12. Some competing tools print a perimeter total automatically; this one leaves the adding to you so the three sides stay the focus.
Yes. Negative values work anywhere in the six fields, and decimals work too. Squaring the differences removes the signs before the square root, so points in any quadrant behave the same way. For example, A (-2, -3), B (4, -3), and C (4, 5) return AB 6.0000, BC 8.0000, and CA 10.0000.
The distances still calculate, but no triangle forms. The tell is in the numbers: the longest distance equals the sum of the other two. With A (0, 0), B (1, 1), and C (2, 2), the tool returns AB 1.4142, BC 1.4142, and CA 2.8284, and 1.4142 + 1.4142 = 2.8284. The verdict badge under the results flags this case as collinear.
Each distance is shown to four decimal places. Underneath, the calculation uses full double precision square roots (the same Math.hypot function used in JavaScript geometry code), so the fourth decimal is a rounded display of a much more precise value. Four decimals is enough to spot exact patterns such as 3, 4, 5 triangles and equal sides.
No. This tool is built for two dimensions: every point has an x and a y coordinate only. If your points have a third coordinate, or if you only need the distance between one pair of points, the general distance calculator on this site covers 2D and 3D pairs as well as latitude and longitude.
All three result fields show "Invalid input". The tool checks that all six coordinates are numbers before it calculates anything, so one missing or mistyped field stops the whole calculation rather than returning two correct sides and one wrong one.
Only in the degenerate cases: the points are collinear, or two of the points are identical, which makes one distance zero. Any three points that are not on one straight line always satisfy the triangle inequality, so the three distances always form a valid triangle. The verdict badge under the results names the case you have.
Add This Calculator to Your Website
References
- Wolfram MathWorld, "Distance" - the Euclidean distance formula in two and three dimensions and its derivation from the Pythagorean theorem. MathWorld: Distance. Accessed October 2026.
- Wolfram MathWorld, "Triangle Inequality" - the rule that any side of a triangle is shorter than the sum of the other two, with equality only for collinear points. MathWorld: Triangle Inequality. Accessed October 2026.
- Wolfram MathWorld, "Heron's Formula" - the area of a triangle from its three side lengths, used in the perimeter and area section. MathWorld: Heron's Formula. Accessed October 2026.
- Khan Academy, "Distance formula" - a lesson deriving the distance formula from the Pythagorean theorem, with practice on coordinate pairs. Khan Academy: Distance Formula. Accessed October 2026.
- MDN Web Docs, "Math.hypot()" - the JavaScript function the calculator uses, which returns the square root of the sum of squares of its arguments. MDN: Math.hypot(). Accessed October 2026.
- OpenStax, Algebra and Trigonometry 2e, "The Rectangular Coordinate Systems and Graphs" - the distance formula in a peer-reviewed open textbook. OpenStax: Rectangular Coordinate Systems and Graphs. Accessed October 2026.