With this website you can find out when you subscribed which YouTube channel.

1 Your channel

Enter the Channel ID or URL of your YouTube channel Please enter a valid YouTube channel ID (e.g. "UCBR8-60-B28hp2BmDPdntcQ") or channel URL (e.g. https://www.youtube.com/user/YouTube).

Where do I find this?

Option 1:
Copy the Channel ID from https://www.youtube.com/account_advanced.

Option 2:
Find the URL of your channel. In the YouTube app, press your profile picture, select "My Channel", in the menu select "Share" and "Copy link". On the website, click your profile picture in the upper right corner, click "Your channel" and copy the link from the address bar.

By using this service you agree to follow YouTube's Terms of Service.

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2 Make your subscriptions public

Go to your Privacy Settings and uncheck "Keep all my subscriptions private". You can undo it again as soon as you've finished using this website.

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Subscriptions

Here you can check how long you've been subscribed to a YouTube channel. YouTube.com doesn't offer a way to show the time you clicked the subscribe button on their website, but for developers, they have an API which returns a list of all subscriptions - with the date you subscribed it!
I made this website because I wanted to know for how long I'm subscribed to my channels and what my first subscription was, but I couldn't find a way to do it. Then I found the way in the API and created this page so everyone can easily use it.