How can I get the canvas size of a custom view outside of the onDraw method?

For drawing purposes, you should not really use the dimensions of the Canvas object.

Just use the dimensions provided to you in the onSizeChanged method. You can either store the dimensions for use in the onDraw method or resize/draw to a backing bitmap that you can draw with later.

Update:

Quickly whipped up some code, it looks like this works:

public class CustomView extends View{
    private Paint paint;
    private int w;
    private int h;

    public CustomView(Context context, AttributeSet attr) {
        super(context, attr);
        paint = new Paint();
        paint.setTextAlign(Align.CENTER);
    }

    @Override
    protected void onSizeChanged(int w, int h, int oldw, int oldh) {
        this.w = w;
        this.h = h;
        super.onSizeChanged(w, h, oldw, oldh);
    }

    @Override
    protected void onDraw(Canvas canvas) {
        canvas.drawColor(Color.WHITE);
        canvas.drawText("TEST", w/2, h/2, paint);   
    }
}

Update 2

Following the circle code update.

We can do this:

   @Override
    protected void onDraw(Canvas canvas) {
        canvas.drawColor(Color.WHITE);
        float centerX = (float) w/2;
        float centerY = (float) h/2;
        float radianAngle = (float) Math.toRadians(startAngle);

        radius[0] = centerX;
        radius[1] = centerY;
        radius[2] = centerX + centerX * FloatMath.cos(radianAngle);
        radius[3] = centerY + centerY * FloatMath.sin(radianAngle);

        paint.setColor(0xFF330000);
        paint.setStrokeWidth(1);
        canvas.drawLines(radius, paint);
    }

You’ll see that this now works on any sized view.