Calculating your distance is straightforward once you know the 3D Distance formula and what each input means. This guide explains the method in plain language, walks through a manual calculation, and gives worked examples you can follow — then you can do it instantly with the 3D Distance Calculator.
What is 3D Distance?
The 3D Distance calculation tells you your distance from a few simple inputs. The figure you are solving for here is the distance.
The 3D Distance formula
The core formula is:
Distance = √((Point 2 — x - Point 1 — x) ^ 2 + (Point 2 — y - Point 1 — y) ^ 2 + (Point 2 — z - Point 1 — z) ^ 2)Here is what each input means:
- Point 1 — x — a number. Example: 1.
- Point 1 — y — a number. Example: 2.
- Point 1 — z — a number. Example: 3.
- Point 2 — x — a number. Example: 4.
- Point 2 — y — a number. Example: 6.
- Point 2 — z — a number. Example: 8.
How to calculate it step by step
- Write down the point 1 — x (for example, 1).
- Write down the point 1 — y (for example, 2).
- Write down the point 1 — z (for example, 3).
- Write down the point 2 — x (for example, 4).
- Write down the point 2 — y (for example, 6).
- Write down the point 2 — z (for example, 8).
- Apply the formula above to get your distance.
- Double-check the result with the 3D Distance Calculator.
Worked examples
Example 1
| Input / Output | Value |
|---|---|
| Point 1 — x | 1 |
| Point 1 — y | 2 |
| Point 1 — z | 3 |
| Point 2 — x | 4 |
| Point 2 — y | 6 |
| Point 2 — z | 8 |
| Distance | 7.071068 |
With point 1 — x of 1, point 1 — y of 2, point 1 — z of 3 and point 2 — x of 4, the distance works out to 7.071068.
Example 2
With point 1 — x of 2, point 1 — y of 2, point 1 — z of 3 and point 2 — x of 4, the distance works out to 6.708204.
| Result | Value |
|---|---|
| Distance | 6.708204 |
Example 3
With point 1 — x of 5, point 1 — y of 2, point 1 — z of 3 and point 2 — x of 4, the distance works out to 6.480741.
| Result | Value |
|---|---|
| Distance | 6.480741 |
Tips for an accurate result
- Keep your units consistent — mixing, say, months with years or grams with kilograms is the most common source of error.
- Round only at the very end. Rounding inputs early can shift the final answer noticeably.
- Re-run the numbers whenever an input changes, rather than estimating from an old result.
Prefer not to do the maths by hand? — the 3D Distance Calculator does it instantly, for free, with the formula and a worked example built in.
Related calculators
Continue exploring math calculators with these tools: Margin of Error Calculator, Sample Size Calculator, Confidence Interval Calculator, Coefficient of Variation Calculator, Regular Heptagon Area Calculator.