can anyone help me find formula, which would correct ABV, that is measured by alcoholmeter, which is calibrated for 20°C, but the mixture has different temperature?

I want to implement this calculation into program so I can not use alcoholometric tables.

I know this formula for density of mixture at 20°C, can it help me?

So e.g. I have measured 50%ABV at 10°C, tables would give me real ABV ==> 53,7%. Now I need to calculate this by formula. I will be very thankful for any help.

Thank you