Distance Calculator

Calculate distances between points, travel distances, and geometric measurements. Perfect for navigation, geometry, physics, and everyday distance calculations.

Calculator Input

Results

Euclidean Distance (2D)
5.0000 units
Straight-line distance in 2D space
Horizontal Distance (Δx):3.0000
Vertical Distance (Δy):4.0000
Manhattan Distance:7.0000
Midpoint:(1.50, 2.00)

Unit Conversions

Meters (if units = m):5.0000 m
Feet (if units = ft):16.4042 ft
Inches (if units = in):196.8505 in

Step-by-Step Calculation

Step 1: Identify the coordinates
Point 1: (0, 0)
Point 2: (3, 4)
Step 2: Calculate the differences
Δx = x₂ - x₁ = 3 - 0 = 3
Δy = y₂ - y₁ = 4 - 0 = 4
Step 3: Apply the distance formula
d = √[(Δx)² + (Δy)²]
d = √[3² + 4²]
d = √[9 + 16]
d = √25
d = 5.0000 units

How to Use

Basic Steps

  1. Select the type of distance calculation you need
  2. Enter the coordinates or values for your points
  3. For geographic distances, use latitude and longitude
  4. For travel calculations, specify distance, speed, and units
  5. 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 = √[(7-3)² + (1-4)²]
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 = Distance ÷ Speed
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).

Using Haversine formula:
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.