How to draw a circle with animation in android with circle size based on a value

You have to draw the circle view, and after that you should create an animation to it.

Creating the circle view:

public class Circle extends View {

    private static final int START_ANGLE_POINT = 90;

    private final Paint paint;
    private final RectF rect;

    private float angle;

    public Circle(Context context, AttributeSet attrs) {
        super(context, attrs);

        final int strokeWidth = 40;

        paint = new Paint();
        paint.setAntiAlias(true);
        paint.setStyle(Paint.Style.STROKE);
        paint.setStrokeWidth(strokeWidth);
        //Circle color
        paint.setColor(Color.RED);

        //size 200x200 example
        rect = new RectF(strokeWidth, strokeWidth, 200 + strokeWidth, 200 + strokeWidth);

        //Initial Angle (optional, it can be zero)
        angle = 120;
    }

    @Override
    protected void onDraw(Canvas canvas) {
        super.onDraw(canvas);
        canvas.drawArc(rect, START_ANGLE_POINT, angle, false, paint);
    }

    public float getAngle() {
        return angle;
    }

    public void setAngle(float angle) {
        this.angle = angle;
    }
}

Creating the animation class to set the new angle:

public class CircleAngleAnimation extends Animation {

    private Circle circle;

    private float oldAngle;
    private float newAngle;

    public CircleAngleAnimation(Circle circle, int newAngle) {
        this.oldAngle = circle.getAngle();
        this.newAngle = newAngle;
        this.circle = circle;
    }

    @Override
    protected void applyTransformation(float interpolatedTime, Transformation transformation) {
        float angle = oldAngle + ((newAngle - oldAngle) * interpolatedTime);

        circle.setAngle(angle);
        circle.requestLayout();
    }
}

Put circle into your layout:

<com.package.Circle
    android:id="@+id/circle"
    android:layout_width="300dp"
    android:layout_height="300dp" />

And finally starting the animation:

Circle circle = (Circle) findViewById(R.id.circle);

CircleAngleAnimation animation = new CircleAngleAnimation(circle, 240);
animation.setDuration(1000);
circle.startAnimation(animation);

The result is:

As extra from @JohnCordeiro answer. I have added parameters from xml to reuse the circle and to fill the circle if needed.

class RecordingCircle(context: Context, attrs: AttributeSet) : View(context, attrs) {

private val paint: Paint
private val rect: RectF

private val fillPaint: Paint
private val fillRect: RectF

var angle: Float
var startAngle: Float

init {
    val typedArray = context.obtainStyledAttributes(attrs, R.styleable.RecordingCircle)
    startAngle = typedArray.getFloat(R.styleable.RecordingCircle_startAngle, 0f)
    val offsetAngle = typedArray.getFloat(R.styleable.RecordingCircle_offsetAngle, 0f)
    val color = typedArray.getColor(R.styleable.RecordingCircle_color, ResourcesCompat.getColor(resources, R.color.recording, null))
    val strokeWidth = typedArray.getFloat(R.styleable.RecordingCircle_strokeWidth, 20f)
    val circleSize = typedArray.getDimension(R.styleable.RecordingCircle_cicleSize, 100f)
    val fillColor = typedArray.getColor(R.styleable.RecordingCircle_fillColor, 0)
    typedArray.recycle()

    paint = Paint().apply {
        setAntiAlias(true)
        setStyle(Paint.Style.STROKE)
        setStrokeWidth(strokeWidth)
        setColor(color)
    }

    rect = RectF(
        strokeWidth,
        strokeWidth,
        (circleSize - strokeWidth),
        (circleSize - strokeWidth)
    )

    fillPaint = Paint().apply {
        setAntiAlias(true)
        setStyle(Paint.Style.FILL)
        setColor(fillColor)
    }

    val offsetFill = strokeWidth
    fillRect = RectF(
        offsetFill,
        offsetFill,
        (circleSize - offsetFill),
        (circleSize - offsetFill)
    )

    //Initial Angle (optional, it can be zero)
    angle = offsetAngle
}

override protected fun onDraw(canvas: Canvas) {
    super.onDraw(canvas)
    if (fillColor > 0) {
        canvas.drawArc(rect, 0f, 360f, false, fillPaint)
    }
    canvas.drawArc(rect, startAngle, angle, false, paint)
}
}

And on the xml:

        <com.myapp.RecordingCircle android:id="@+id/cameraRecordButton"
        android:layout_width="match_parent"
        android:layout_height="match_parent"
        app:offsetAngle="360"
        app:color="@color/light_grey"
        app:strokeWidth="10"
        app:cicleSize="@dimen/camera_record_button"
        app:fillColor="@color/recording_bg" />

    <com.myapp.RecordingCircle android:id="@+id/progress"
        android:layout_width="match_parent"
        android:layout_height="match_parent"
        app:startAngle="270"
        app:color="@color/recording"
        app:strokeWidth="10"
        app:cicleSize="@dimen/camera_record_button" />

Here the result: Note the semi-transparent fill of the button