Distance Calculator
Adjust the inputs below. Results update as you type.
How it works
Haversine formula: d = 2r × arcsin(√(sin²(Δlat/2) + cos(lat₁)cos(lat₂)sin²(Δlon/2))). Earth's mean radius is 6,371 km. This gives the great-circle distance, which differs from driving distance due to roads. 1 nautical mile = 1 minute of arc of latitude = 1.852 km. For driving distances, use a routing API that accounts for road networks.
Input guidance
- Check units and decimal placement before running calculations.
- For percentage and ratio tasks, define the baseline value clearly.
- Use rounded output carefully and keep full precision for intermediate steps.
The formula
Between two points, distance = √((x₂ − x₁)² + (y₂ − y₁)²), the Pythagorean theorem applied to coordinates. In 3-D, add the (z₂ − z₁)² term.
Worked example
From (1, 2) to (4, 6): √((3)² + (4)²) = √(9 + 16) = √25 = 5 units.
More examples to test
- Baseline example: solve with clean numbers first to verify formula direction.
- Edge-case example: test near-zero or boundary values to avoid interpretation errors.
How to interpret results
Use outputs as quick checks, then verify with step-by-step work for graded or high-stakes use.
When this can be inaccurate
Errors usually come from unit mismatch, wrong baseline assumptions, or rounding too early in multistep problems.
Change history
- July 2026: Quality-reviewed for publication with formula checks and explanatory copy updates.
Site-wide corrections also appear on the corrections log.
Build math and logic skills with guided lessons
Educational platform recommendation.
Frequently asked questions
How is straight-line distance found?+
With the distance formula, which is the Pythagorean theorem: the square root of the sum of squared coordinate differences.
Does this work in 3-D?+
Yes. Add the squared difference of the z-coordinates inside the square root for three-dimensional distance.
What about distance on a map?+
For latitude/longitude, the haversine formula accounts for Earth's curvature, which the flat distance formula ignores.
Why do my classroom and calculator results differ?+
Differences usually come from rounding conventions, order-of-operations handling, or different baseline assumptions.
What is the safest way to validate an answer?+
Recompute with units shown and check against a second method or manual arithmetic for critical problems.