When using location services in Day One, the weather is automatically added to the entry as well. Here is how to change from Fahrenheit to Celsius:

iOS: 

Go to Day One > Settings > Advanced > toggle the option for Fahrenheit. Turning this off will enable Celsius. 

You can also change the weather service used in Day One iOS. Tap Weather Service in that same menu. Forecast.io provides more accurate weather information in US and UK. 

Android:

Go to Day One > Settings > Units. Switch between Imperial and Metric. 

macOS:

Go to Day One > Preferences > Appearance > uncheck the option for Fahrenheit.

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