How to find horizontal distance from coordinate differences
East and north coordinate differences form two perpendicular sides of a right triangle. The straight horizontal distance between the points is its hypotenuse.
What the formula is saying
Use the Pythagorean theorem: square ΔE, square ΔN, add them and take the square root. Differences can be negative; squaring removes their signs for distance.
Read the symbols in plain language
- ΔE
- Easting differencem
- ΔN
- Northing differencem
Sort out the units first
Enter coordinate differences in metres on the same planar coordinate system. The result is in metres; latitude/longitude degrees cannot be used directly.
Let’s solve one together
Read the given values, follow each operation, then check what the result means.
- ΔE · Easting difference
- 30 m
- ΔN · Northing difference
- 40 m
Square the east difference
This is one perpendicular side squared.
(30)^2 = 900 m²Add the north difference squared
Adding squares combines the perpendicular components.
(900) + (40)^2 = 2500 m²Take the square root
Return from squared metres to metres.
√((2500)) = 50 m
Does this worked answer make sense?
The result cannot be smaller than either component magnitude. The 30–40–50 example is a scaled 3–4–5 triangle.
Now try your own values
Change a value or its unit. The same method will show your calculation, step by step.
Results update only when you calculate. The lesson example above stays unchanged.
Your turn — check your understanding
Use these new values. Work it out first, then check your answer.
- ΔE · Easting difference
- 60 m
- ΔN · Northing difference
- 80 m
Find: horizontal distance from coordinate differences
A hint, not the answer
Use the Pythagorean theorem: square ΔE, square ΔN, add them and take the square root. Differences can be negative; squaring removes their signs for distance.
Enter coordinate differences in metres on the same planar coordinate system. The result is in metres; latitude/longitude degrees cannot be used directly.
Show the full practice solution
Compare the steps with your work; revealing a solution does not mark the lesson complete.
Square the east difference
This is one perpendicular side squared.
(60)^2 = 3600 m²Add the north difference squared
Adding squares combines the perpendicular components.
(3600) + (80)^2 = 10000 m²Take the square root
Return from squared metres to metres.
√((10000)) = 100 m
Avoid the common trap
Adding |ΔE| + |ΔN| measures a two-leg path, not the straight line. Do not confuse horizontal distance with sloping distance.
When this method applies — and when it does not
Planar coordinate geometry. Projection scale, elevation and geodetic distance corrections are outside this lesson.
For study and understanding, not approval of a real structure, site operation or design. Apply the correct standard, National Annex and professional review to actual engineering work.
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Sources & further reading
References open in a new tab and explain the underlying principles. The teaching text and examples here are SimpleFlick’s own; the source organisations have not endorsed this calculator.
Lesson updated: · Worked examples checked against the implemented formula; not an independent engineering certification.