Yes, there is an equation that can be used to calculate the phases of the moon. It is called the "Lunar Phase Formula" and it takes into account the position of the moon relative to the sun and the earth.

Here are the steps to calculate the phase of the moon using the Lunar Phase Formula:

1. Determine the date for which you want to calculate the phase of the moon.
2. Calculate the number of days since the last new moon. This is known as the "Julian Date" and can be calculated using a formula or found online.
3. Calculate the number of days since the last full moon. This can also be found online or calculated using a formula.
4. Subtract the number of days since the last full moon from the number of days since the last new moon. This will give you the number of days since the last quarter moon.
5. Divide the number of days since the last quarter moon by 29.53 (the length of a lunar cycle in days).
6. Take the remainder of the division and multiply it by 360. This will give you the angle of the moon in its orbit around the earth.
7. Use the angle to determine the phase of the moon. For example, if the angle is between 0 and 90 degrees, it is a waxing crescent. If it is between 90 and 180 degrees, it is a waxing gibbous. And so on.

There are also many online calculators and apps that can do this calculation for you automatically.