TFT

Distance Formula Calculator – Find Distance Between Two Points

Calculate the straight-line distance between any two points on a coordinate plane. Enter the x and y coordinates to get the distance and midpoint instantly.

d = √[(x₂-x₁)² + (y₂-y₁)²]
How It Works

Step 1: Enter the coordinates of your first point (x₁, y₁) in the input fields.

Step 2: Enter the coordinates of your second point (x₂, y₂).

Step 3: Click Calculate to see the distance and the midpoint between the two points.

Why Use the Distance Formula

Geometry and Coordinate Systems

The distance formula comes directly from the Pythagorean theorem. It gives you the straight-line distance between any two points on a plane, which is fundamental to geometry, navigation, and physics.

Real-World Applications

Map applications use this formula to calculate distances between locations. Game developers use it for collision detection. Surveyors use it to measure property boundaries. It's everywhere once you start looking.

Midpoint Calculation

The midpoint formula finds the exact center point between two coordinates. This is useful for finding meeting points, dividing segments equally, or locating the center of geometric shapes.

No Manual Calculation Needed

Square roots and squaring can get messy with decimals or negative numbers. This calculator handles all the arithmetic, so you can focus on understanding the concepts instead of crunching numbers.

Distance Formula Reference

The Formula

d = √[(x₂ - x₁)² + (y₂ - y₁)²]

Where (x₁, y₁) is the first point and (x₂, y₂) is the second point.

Worked Example

Find the distance between (1, 2) and (5, 6):

d = √[(5 - 1)² + (6 - 2)²]

d = √[4² + 4²]

d = √[16 + 16]

d = √32

d ≈ 5.6569

Midpoint Formula

M = ((x₁ + x₂)/2, (y₁ + y₂)/2)

The midpoint is simply the average of the x-coordinates and the average of the y-coordinates.

Practice Problems
Point 1Point 2DistanceMidpointAction
(0, 0)(3, 4)5.0000(1.5, 2)
(1, 2)(5, 6)5.6569(3, 4)
(-2, -3)(2, 3)7.2111(0, 0)
(5, -1)(-3, 4)9.4340(1, 1.5)

Click "Load" to try any example in the calculator above.

Frequently Asked Questions

What is the distance formula?
The distance formula calculates the straight-line distance between two points on a coordinate plane: d = √[(x₂-x₁)² + (y₂-y₁)²]. It's derived from the Pythagorean theorem (a² + b² = c²).
Can the distance be negative?
No. Distance is always positive or zero. The formula squares the differences, which makes negative values positive. The square root of a positive number is always positive.
How do you find the midpoint?
The midpoint formula is M = ((x₁+x₂)/2, (y₁+y₂)/2). You average the x-coordinates to get the x-coordinate of the midpoint, and average the y-coordinates to get the y-coordinate.
Does this work in 3D space?
This calculator handles 2D coordinates. For 3D, add the z-term: d = √[(x₂-x₁)² + (y₂-y₁)² + (z₂-z₁)²]. The midpoint formula also extends to three dimensions.
Why is the distance formula useful?
It's fundamental to geometry, physics, computer graphics, GPS navigation, and game development. Any time you need to measure how far apart two things are on a plane, this is the formula.

Other Free Tools

Pythagorean Theorem Calculator

Pythagorean Theorem Calculator

Slope Calculator

Slope Calculator

Linear Equation Solver

Linear Equation Solver – Solve ax + b = 0

0 100 Acceleration Estimator

0-100 Acceleration Estimator – Calculate 0 to 100 km/h Time

1rm Calculator

1RM Calculator – Calculate Your One Rep Max for Any Lift

4 Percent Rule Retirement Calculator

4% Rule Retirement Calculator