UIImageView *iv; // your image view
CGSize imageSize = iv.image.size;
CGFloat imageScale = fminf(CGRectGetWidth(iv.bounds)/imageSize.width, CGRectGetHeight(iv.bounds)/imageSize.height);
CGSize scaledImageSize = CGSizeMake(imageSize.width*imageScale, imageSize.height*imageScale);
CGRect imageFrame = CGRectMake(roundf(0.5f*(CGRectGetWidth(iv.bounds)-scaledImageSize.width)), roundf(0.5f*(CGRectGetHeight(iv.bounds)-scaledImageSize.height)), roundf(scaledImageSize.width), roundf(scaledImageSize.height));

@import AVFoundation;

AVMakeRectWithAspectRatioInsideRect(imageView.image.size, imageView.bounds);

CGRectIntegral(…)

if you want to calculate it yourself, use below code written by me.

func getImageFrameInImageView(imageView : UIImageView) -> CGRect {
    /*
    by 徐明刚， ericxu1983@163.com
    算法：
        设高宽比 r = h/w, 则：r(imageView) 缩写成r(v), r(image)缩写为r(i),
        if r(i) > r(v), 则
        h(i) = h(v),
        h(i) / w(i) = r(i) -> w(i) = h(i) / r(i)
        y = 0
        x = (w(v) / 2)  - (w(i) / 2)
    反之
    */

    let image = imageView.image!
    let wi = image.size.width
    let hi = image.size.height
    print("wi:(wi), hi:(hi)")

    let wv = imageView.frame.width
    let hv = imageView.frame.height
    print("wv:(wv), hv:(hv)")

    let ri = hi / wi
    let rv = hv / wv
    print("ri:(ri), rv:(rv)")

    var x, y, w, h: CGFloat

    if ri > rv {
        h = hv
        w = h / ri
        x = (wv / 2) - (w / 2)
        y = 0
    } else {
        w = wv
        h = w * ri
        x = 0
        y = (hv / 2) - (h / 2)
    }

    return CGRect(x: x, y: y, width: w, height: h)
}

let frameIdentifyBorderView = UIView(frame: imageFrameInImageView)
    frameIdentifyBorderView.layer.borderWidth = 3
    frameIdentifyBorderView.layer.borderColor = UIColor.blueColor().CGColor

    imageView.addSubview(frameIdentifyBorderView)

import UIKit
import AVFoundation

class ViewController: UIViewController {

    var imageView = UIImageView()
    override func viewDidLoad() {
        super.viewDidLoad()
        // Do any additional setup after loading the view, typically from a nib.
        imageView.frame = self.view.bounds
        imageView.contentMode = .scaleAspectFit
        imageView.backgroundColor = .blue
        imageView.autoresizingMask = [.flexibleWidth,.flexibleHeight]
        self.view.addSubview(imageView)
    }

    override func viewWillAppear(_ animated: Bool) {
        super.viewWillAppear(animated)

        URLSession.shared.dataTask(with: URL(string: "https://images.pexels.com/photos/248797/pexels-photo-248797.jpeg?w=940&h=650&dpr=2&auto=compress&cs=tinysrgb")!) { (data, response, error) in
            guard let dt = data else{print("error");return}
            DispatchQueue.main.async {
                guard let image = UIImage(data: dt) else{print("error");return}
                self.imageView.image = image
                self.imageView.layoutIfNeeded()
                let realImageRect = AVMakeRect(aspectRatio: image.size, insideRect: self.imageView.bounds)


                //proof
                let view = UIView(frame: realImageRect)
                view.layer.borderColor = UIColor.green.cgColor
                view.layer.borderWidth = 3
                self.view.addSubview(view)
            }
        }.resume()
    }
}