I woke up in a state of janāba without having washed. Is my fast valid?

This worries people a great deal in a first Ramadan and has a clear, reassuring answer.

The validity of the fast does not depend on being in a state of major purity when the day begins. It depends on the intention and on abstaining from food, drink and intimacy from dawn until sunset.

The fasting verse itself permits intimacy throughout the whole night of Ramadan: “It has been made permissible for you the night preceding fasting to go to your wives for sexual relations. They are a clothing for you and you are a clothing for them. Allah knows that you used to deceive yourselves, so He accepted your repentance and forgave you. So now, have relations with them and seek that which Allah has decreed for you i.e., offspring. And eat and drink until the white thread of dawn becomes distinct to you from the black thread of night. Then complete the fast until the night i.e., sunset. And do not have relations with them as long as you are staying for worship in the mosques. These are the limits set by Allah, so do not approach them. Thus does Allah make clear His verses i.e., ordinances to the people that they may become righteous.” (Qur’an 2:187)

And if it is permitted until dawn, then waking without having washed obviously had to be valid; otherwise the permission would make no practical sense. It is also reported that the Prophet ﷺ would wake in that state and fast.

In practice:

• The fast is valid. Nothing is made up.
• The ghusl is done afterwards, without anxious haste, but before praying: the prayer does require the purification.
• It should not be delayed past sunrise, because that would mean missing Fajr, which is a separate matter and that one is serious.
• For a woman whose period ends in the night: if it ended before dawn, she fasts that day even if there was no time to wash.

The distinction that orders all of this: fasting and prayer have different requirements. Major purity is a condition of the prayer, not of the fast.