Distance Calculator
Calculate distances between points, travel distances, and geometric measurements. Perfect for navigation, geometry, physics, and everyday distance calculations.
Calculator Input
Results
Unit Conversions
Step-by-Step Calculation
How to Use
Basic Steps
- Select the type of distance calculation you need
- Enter the coordinates or values for your points
- For geographic distances, use latitude and longitude
- For travel calculations, specify distance, speed, and units
- Review the calculated distance and conversions
Distance Types
- 2D: Euclidean distance in a plane
- 3D: Euclidean distance in 3D space
- Geographic: Great circle distance on Earth
- Manhattan: Grid-based city block distance
- Travel: Time and speed calculations
- Speed: Solve for speed, distance, or time
Understanding Distance Calculations
Euclidean Distance
The straight-line distance between two points, calculated using the Pythagorean theorem.
2D: d = √[(x₂-x₁)² + (y₂-y₁)²]
3D: d = √[(x₂-x₁)² + (y₂-y₁)² + (z₂-z₁)²]
Most commonly used for geometric calculations and coordinate systems.
Geographic Distance
The shortest distance between two points on Earth's surface, using the Haversine formula.
Accounts for Earth's curvature
Uses latitude and longitude coordinates
Results in great circle distance
Essential for navigation, GPS systems, and geographic analysis.
Manhattan Distance
Also known as "taxicab distance" or "city block distance." Calculates the distance you would travel in a city with a grid layout.
d = |x₂-x₁| + |y₂-y₁|
Useful for urban planning, logistics, and situations where you can only move along grid lines.
Example Calculations
Example 1: 2D Distance
Problem: Find the distance between points (3, 4) and (7, 1).
d = √[4² + (-3)²]
d = √[16 + 9]
d = √25 = 5 units
Answer: The distance is 5 units.
Example 2: Travel Time
Problem: How long to travel 150 km at 60 km/h?
Time = 150 km ÷ 60 km/h
Time = 2.5 hours
Answer: It takes 2.5 hours (2 hours 30 minutes).
Example 3: Geographic Distance
Problem: Distance between New York (40.7128°N, 74.0060°W) and London (51.5074°N, 0.1278°W).
Great circle distance ≈ 5,585 km
≈ 3,470 miles
Answer: The distance is approximately 5,585 kilometers.
Frequently Asked Questions
What's the difference between Euclidean and Manhattan distance?
Euclidean distance is the straight-line distance ("as the crow flies"), while Manhattan distance is the sum of horizontal and vertical distances (like walking city blocks). Manhattan distance is always greater than or equal to Euclidean distance.
How accurate is geographic distance calculation?
The Haversine formula assumes Earth is a perfect sphere, which gives results accurate to within 0.5% for most purposes. For higher precision, more complex ellipsoidal models can be used.
Can I calculate distance in different units?
Yes! The calculator automatically converts between common units like kilometers, miles, meters, and feet. Choose the units that work best for your specific application.