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Calculate Position From Angle and Distance

Reviewed by Calculator Editorial Team

This calculator helps you determine a new position (coordinates) when you know the starting point, the angle of movement, and the distance traveled. It's useful for navigation, robotics, and any application requiring coordinate calculations based on direction and distance.

How to Use This Calculator

To calculate a new position from an angle and distance:

  1. Enter the starting coordinates (X and Y)
  2. Enter the angle of movement in degrees
  3. Enter the distance to travel
  4. Select the unit for distance (meters, kilometers, miles, etc.)
  5. Click "Calculate" to get the new coordinates

The calculator will display the new position (X and Y coordinates) and show the movement on a simple chart.

Formula

The new position is calculated using basic trigonometry:

New X = Original X + (Distance × cos(Angle in radians)) New Y = Original Y + (Distance × sin(Angle in radians))

Where:

  • Original X and Y are the starting coordinates
  • Distance is the length of movement
  • Angle is converted from degrees to radians (π/180 × degrees)

Note: Angles are measured from the positive X-axis (east direction) in the standard mathematical coordinate system.

Worked Example

Let's say you start at position (10, 20), move 15 meters at 45 degrees from the positive X-axis.

  1. Convert 45 degrees to radians: 45 × (π/180) ≈ 0.785 radians
  2. Calculate the change in X: 15 × cos(0.785) ≈ 10.606 meters
  3. Calculate the change in Y: 15 × sin(0.785) ≈ 10.606 meters
  4. New X = 10 + 10.606 ≈ 20.606
  5. New Y = 20 + 10.606 ≈ 30.606

The new position would be approximately (20.606, 30.606).

Frequently Asked Questions

What angle should I use for north, south, east, and west?
East is 0 degrees, north is 90 degrees, west is 180 degrees, and south is 270 degrees. Angles increase counterclockwise from the positive X-axis.
Can I use negative angles?
Yes, negative angles represent clockwise rotation from the positive X-axis. For example, -90 degrees is equivalent to 270 degrees.
What if my distance is in miles but I want the result in meters?
Select "miles" as the unit and the calculator will convert the distance to meters before performing the calculation. The result will be in meters.
Is this calculator accurate for large distances?
This calculator uses basic trigonometry and assumes a flat plane. For very large distances or curved surfaces, more advanced calculations would be needed.