How to create a circular progress indicator for a count down timer

You can do it using CAShapeLayer and animating the stroke end as follow:

update Xcode 9 • Swift 4

define the time left

let timeLeftShapeLayer = CAShapeLayer()
let bgShapeLayer = CAShapeLayer()
var timeLeft: TimeInterval = 60
var endTime: Date?
var timeLabel =  UILabel()
var timer = Timer()
// here you create your basic animation object to animate the strokeEnd
let strokeIt = CABasicAnimation(keyPath: "strokeEnd")

define a method to create de UIBezierPath

startAngle at -90˚ and endAngle 270

func drawBgShape() {
    bgShapeLayer.path = UIBezierPath(arcCenter: CGPoint(x: view.frame.midX , y: view.frame.midY), radius:
        100, startAngle: -90.degreesToRadians, endAngle: 270.degreesToRadians, clockwise: true).cgPath
    bgShapeLayer.strokeColor = UIColor.white.cgColor
    bgShapeLayer.fillColor = UIColor.clear.cgColor
    bgShapeLayer.lineWidth = 15
    view.layer.addSublayer(bgShapeLayer)
}
func drawTimeLeftShape() {
    timeLeftShapeLayer.path = UIBezierPath(arcCenter: CGPoint(x: view.frame.midX , y: view.frame.midY), radius:
        100, startAngle: -90.degreesToRadians, endAngle: 270.degreesToRadians, clockwise: true).cgPath
    timeLeftShapeLayer.strokeColor = UIColor.red.cgColor
    timeLeftShapeLayer.fillColor = UIColor.clear.cgColor
    timeLeftShapeLayer.lineWidth = 15
    view.layer.addSublayer(timeLeftShapeLayer)
}

add your Label

func addTimeLabel() {
    timeLabel = UILabel(frame: CGRect(x: view.frame.midX-50 ,y: view.frame.midY-25, width: 100, height: 50))
    timeLabel.textAlignment = .center
    timeLabel.text = timeLeft.time
    view.addSubview(timeLabel)
}

at viewDidload set the endTime and add your CAShapeLayer to your view:

override func viewDidLoad() {
    super.viewDidLoad()
    view.backgroundColor = UIColor(white: 0.94, alpha: 1.0)
    drawBgShape()
    drawTimeLeftShape()
    addTimeLabel()
    // here you define the fromValue, toValue and duration of your animation
    strokeIt.fromValue = 0
    strokeIt.toValue = 1
    strokeIt.duration = timeLeft
    // add the animation to your timeLeftShapeLayer
    timeLeftShapeLayer.add(strokeIt, forKey: nil)
    // define the future end time by adding the timeLeft to now Date()
    endTime = Date().addingTimeInterval(timeLeft)
    timer = Timer.scheduledTimer(timeInterval: 0.1, target: self, selector: #selector(updateTime), userInfo: nil, repeats: true)
}

when updating the time

@objc func updateTime() {
    if timeLeft > 0 {
        timeLeft = endTime?.timeIntervalSinceNow ?? 0
        timeLabel.text = timeLeft.time
    } else {
        timeLabel.text = "00:00"
        timer.invalidate()
    }
}

you can use this extension to convert the degrees to radians and display time

extension TimeInterval {
    var time: String {
        return String(format:"%02d:%02d", Int(self/60),  Int(ceil(truncatingRemainder(dividingBy: 60))) )
    }
}
extension Int {
    var degreesToRadians : CGFloat {
        return CGFloat(self) * .pi / 180
    }
}

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Sample project