I am currently developing a new 2D mobile game with the Unity game engine. There were no problem until I needed mathematics. Indeed, I need to calcul thespeed of rotation of a circle to make 180° in a given distance and speed. I will show you how you can calculate this speed in C# and adding it to you animation.

Here are the informations we know for having the result you can see on the left

  • Distance : d = 5m
  • Speed of the circle : v = 2m/s
  • Rotation from start to end : 180°
  • Radius of the circle : 0.5m

On the paper

First, you need to know the time to travel the distance : t = d/v = 5/2 = 2.5s

Then, you need to make 180° in 2.5 second. That equal to pi/radian=180°

The speed of the rotation is : pi/time = pi/2.5 rad/sec = 1.256

To convert that speed of rotation (1.256) in m/s you need to calculate:
speed rotation * radius = 1.256 * 0.5 = 0.0628m/s

That’s it for the « paper » version.

In C#

I will assume that you already set an animator with a rotation animation for your gameobject.

Here are the settings I am using to rotate the player from 180° to the left and to the right
  • In your animator controller, add a new parameter as float called « rotationSpeed ».
  • In your animation settings, check « parameters » under « Speed > multiplier » and select rotationSpeed.

Don’t forget to uncheck « Loop time » for your rotation animation.

float time;
float playerSpeed = 2f;
flaot distance = 5f;
float radius = 0.5 


/*** FUNCTION UPDATE ***/
// Time needed to travel the distance: 
time = distance / playerSpeed;

// Get the rotation speed, convert it in m/s and set the value to the rotationSpeed. It will speed the animation
animator.SetFloat ("rotationSpeed", (Mathf.PI / time) * radius);

// Play the rotation animation
animator.Play ("rotationToLeft");


I hope it will help many of you 🙂