3-4-5 distance
(1, 2) to (4, 6)delta x 3, delta y 4, distance squared 25, and distance 5 units
Distance Calculator
Use this free coordinate distance calculator to enter two 2D points and find straight-line distance, distance squared, delta x, delta y, midpoint, and formula substitution.
Unit-aware inputsFormula noteExample numbersTab-only history
Point distance5 cm
- Delta x
- 3
- Delta y
- 4
- Distance squared
- 25 cm^2
- Midpoint
- (2.5, 4)
Steps
- Find delta x: 4 - 1 = 3.
- Find delta y: 6 - 2 = 4.
- Square and add: (3)^2 + (4)^2 = 25.
- Take the square root: d = sqrt(25) = 5 cm.
Recent answers
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Privacy note
Geometry answers and history stay in this browser tab while you work.
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How to use the Distance Calculator
- Enter the first point as x1 and y1.
- Enter the second point as x2 and y2.
- Press Calculate distance to see delta x, delta y, distance squared, midpoint, and the final distance.
- Check the substituted square-and-add line before taking the square root or copying the result.
- Use this 2D coordinate result for a straight line, not a road, walking route, or GPS path.
What people use it for
Find straight-line distance between two points on a coordinate plane.
Check delta x, delta y, distance squared, and midpoint while working coordinate geometry problems.
Compare coordinate distance with slope, rise, run, and right-triangle side lengths.
Use the formula steps to spot sign mistakes before copying an answer into notes or homework.
Label the answer with the same unit as the coordinates, such as meters, feet, miles, or grid units.
Quick examples
Origin to point
(0, 0) to (8, 15)17 units
Negative coordinates
(-3, 4) to (5, -2)10 units; signs change the deltas before squaring
Same x-value
(3, -2) to (3, 7)9 units with midpoint (3, 2.5)
Non-perfect square
(2, 1) to (7, 4)distance squared 34, so distance is sqrt(34), about 5.8309518949 units
Need the guide or a nearby tool?
Need a slower walkthrough, a related calculator, or the full library? These links keep you close to the task you started.
- How to use the Distance CalculatorSee slower examples, input meanings, formula notes, result limits, and mistakes to avoid.
- CalculatorsBrowse related calculators and utilities in the same category.
- Calculator and utility guidesFind more guides that use real tool inputs and example numbers.
- All free toolsSearch every live tool, converter, calculator, AI helper, and browser utility.
Frequently asked questions
Quick answers about formulas, units, valid measurements, examples, copying, and private in-browser history.
What formula does the Distance Calculator use?
The calculator subtracts x1 from x2 to get delta x, subtracts y1 from y2 to get delta y, squares both changes, adds the squares, then takes the square root: d = sqrt((x2 - x1)^2 + (y2 - y1)^2). This is the straight-line distance formula for two points in a flat coordinate plane.
What do x1, y1, x2, and y2 mean?
x1 and y1 are the first point. x2 and y2 are the second point. Enter the coordinates in the same scale and unit so the distance label is meaningful.
What do the main Distance Calculator inputs mean?
The main inputs are the numbers, operation, mode, or known values the calculator needs. Keep units consistent, enter percentages the way the page label shows, and use the examples as a quick check before trusting the answer.
How should I read the Distance Calculator answer?
Read the headline answer, then check the supporting lines and examples to understand how the calculator got there. If one input changes, rerun the tool and compare the new answer instead of guessing.
What should I double-check before trusting the Distance Calculator?
Check units, signs, rounding, and the selected mode before copying the answer. If the number feels weird, rerun one of the examples first, then put your own values back in slowly.
Why does the calculator show delta x and delta y?
Delta x is x2 - x1, and delta y is y2 - y1. They show the horizontal and vertical changes before the calculator squares them, which makes sign mistakes easier to catch.
What does distance squared mean?
Distance squared is delta x squared plus delta y squared before the final square root. It is 25 for the points (1, 2) and (4, 6), so the distance is sqrt(25) = 5. This intermediate value helps you check the substitution and keep an exact square-root form for non-perfect squares.
Can distance be negative?
No. Distance is a length, so it is zero or positive. Delta x or delta y can be negative, but the formula squares those changes before it takes the square root.
Does it show midpoint?
Yes. It shows midpoint as ((x1 + x2) / 2, (y1 + y2) / 2), so you can find the point halfway between the two coordinates.
Can I use negative or decimal coordinates?
Yes. Negative numbers and decimals work as long as each coordinate is a valid number and all coordinates use the same scale.
What happens if the two points are the same?
The distance is 0 because there is no change in x or y. The midpoint is the same coordinate because both endpoints are identical.
What units does the answer use?
The answer uses the unit label you enter. If your coordinates are in meters, the distance is in meters. If they are grid units, the result is in grid units. The label is text only, not a unit converter.
Should I use this or the Slope Calculator?
Use Distance Calculator for the straight-line length between points. Use Slope Calculator for steepness, rise, run, and line equations from the same pair of points.
How is this related to the Pythagorean theorem?
The distance formula is the Pythagorean theorem applied to coordinate changes. Delta x and delta y act like the two legs of a right triangle, and the distance is the hypotenuse.
Can this calculate driving distance or GPS route distance?
No. This is straight-line coordinate distance. It does not follow roads, trails, map routes, elevation changes, traffic, or GPS paths.
Can it calculate 3D distance?
No. This page is for two-dimensional points only. A 3D distance formula also needs z1 and z2, which should be handled as a separate mode with clear labels.
When should I not rely on this distance answer by itself?
Use it as a coordinate-geometry check, not an exact field survey, route estimate, construction measurement, or safety decision. Double-check the coordinate scale, signs, units, and rounding, and use calibrated measurement, GIS data, or professional plans when the limit matters.
Is my distance history private?
Yes. Recent distance answers stay only in the current browser tab while you use the page. They are not sent to a server.