Distance Formula Calculator
Distance and midpoint between two coordinates.
Enter your values
Enter the x₁ you are working with.
Enter the y₁ you are working with.
Enter the z₁ you are working with.
Enter the x₂ you are working with.
Enter the y₂ you are working with.
Enter the z₂ you are working with.
Results update instantly as you type — no submit needed. Your values are remembered on this device, and the shareable link reopens the calculator with exactly these numbers.
- Distance
- 10
- Midpoint
- (4, 6)
- Δx, Δy, Δz
- 6, 8, 0
- Distance squared
- 100
Working
- 1d = √(6² + 8²) = 10
Quick answer
The distance between two points is √((x₂−x₁)² + (y₂−y₁)²), a direct application of Pythagoras.
d = √((x₂−x₁)² + (y₂−y₁)² + (z₂−z₁)²)
At a glance
| What it does | Distance and midpoint between two coordinates. |
|---|---|
| Category | Math |
| Inputs needed | x₁, y₁, z₁, x₂, y₂, z₂ |
| Main output | Distance |
| Formula | d = √((x₂−x₁)² + (y₂−y₁)² + (z₂−z₁)²) |
| Cost | Free — no sign-up, no download |
How to use the Distance Formula Calculator
- 1Enter the first point's coordinates.
- 2Enter the second point.
- 3Leave z at 0 for 2D problems.
Inputs explained
- x₁
- Enter the x₁ you are working with.
- y₁
- Enter the y₁ you are working with.
- z₁
- Enter the z₁ you are working with.
- x₂
- Enter the x₂ you are working with.
- y₂
- Enter the y₂ you are working with.
- z₂
- Enter the z₂ you are working with.
Worked example
Using the values the calculator loads with:
Inputs
- x₁1
- y₁2
- z₁0
- x₂7
- y₂10
- z₂0
Results
- Distance10
- Midpoint(4, 6)
- Δx, Δy, Δz6, 8, 0
- Distance squared100
- d = √(6² + 8²) = 10
Frequently asked questions
Is this the same as Pythagoras?
Yes. The distance formula is the Pythagorean theorem applied to the horizontal and vertical differences.
Does it work in 3D?
Yes — just add the z term under the square root, which this calculator does automatically.
What do I need to enter into the Distance Formula Calculator?
Just 6 values: x₁, y₁, z₁, x₂, y₂, z₂. Every field starts with a realistic example, so you can change one number at a time and watch the result update instantly.
How does the Distance Formula Calculator work out the answer?
The distance between two points is √((x₂−x₁)² + (y₂−y₁)²), a direct application of Pythagoras. It applies the formula d = √((x₂−x₁)² + (y₂−y₁)² + (z₂−z₁)²) and shows the working so you can check each step by hand.
Is the Distance Formula Calculator free, and do I need an account?
It is completely free with no sign-up, no download and no usage limit. Everything is calculated in your browser, so the numbers you type never leave your device.
Results are estimates for general information. For medical, legal, structural or financial decisions, confirm with a qualified professional.