Short answer
More than we can picture. The Prophet ﷺ said Allah made mercy in a hundred parts and sent down one, from which all creatures show kindness to each other; He kept ninety-nine for the Day of Judgement. He also said Allah is more merciful to His servants than a mother to her child.
Mercy is a true attribute of Allah, affirmed as befits Him, without the softness or change found in creatures. Hoping in His mercy is required of every believer, and despairing of it is a major sin.
The four schools agree on this.
Explanation
Every surah but one begins with "In the name of Allah, the Entirely Merciful, the Especially Merciful". Ar-Rahman points to mercy that reaches all of creation in this world, and ar-Rahim to the special mercy He gives the believers, above all in the Hereafter. Allah says, "My mercy encompasses all things" (7:156), and "Your Lord has decreed upon Himself mercy" (6:54).
The Prophet ﷺ described its size in plain pictures. Allah made mercy a hundred parts, kept ninety-nine and sent one to earth; from that one part an animal lifts its hoof away from its young (Sahih Muslim). Seeing a mother among the captives clutch her baby to her chest, he asked whether she would throw her child into a fire. When the Companions said no, he said Allah is more merciful to His servants than she is to her child (Sahih al-Bukhari). He also said Allah wrote, "My mercy prevails over My wrath".
He went further: if the disbeliever knew all the mercy that is with Allah, he would not lose hope of Paradise, and if the believer knew all the punishment with Allah, he would not feel safe from the Fire (Sahih al-Bukhari). Mercy and justice sit together. The same verse that says His mercy covers everything adds that He will decree it especially for those who fear Him and give zakah.
So no sin is too big to bring back to Him (39:53). Repent, and hope. Read Does Allah forgive all sins? and the meanings of ar-Rahman and ar-Rahim.
The evidence
Quran, Surah Al-A'raaf 7:156
۞ وَٱكْتُبْ لَنَا فِى هَٰذِهِ ٱلدُّنْيَا حَسَنَةًۭ وَفِى ٱلْءَاخِرَةِ إِنَّا هُدْنَآ إِلَيْكَ ۚ قَالَ عَذَابِىٓ أُصِيبُ بِهِۦ مَنْ أَشَآءُ ۖ وَرَحْمَتِى وَسِعَتْ كُلَّ شَىْءٍۢ ۚ فَسَأَكْتُبُهَا لِلَّذِينَ يَتَّقُونَ وَيُؤْتُونَ ٱلزَّكَوٰةَ وَٱلَّذِينَ هُم بِـَٔايَٰتِنَا يُؤْمِنُونَ ﴿١٥٦﴾
And decree for us in this world [that which is] good and [also] in the Hereafter; indeed, we have turned back to You." [Allah] said, "My punishment - I afflict with it whom I will, but My mercy encompasses all things." So I will decree it [especially] for those who fear Me and give zakah and those who believe in Our verses -
Allah's mercy reaches everything.
Quran, Surah Al-An'aam 6:54
وَإِذَا جَآءَكَ ٱلَّذِينَ يُؤْمِنُونَ بِـَٔايَٰتِنَا فَقُلْ سَلَٰمٌ عَلَيْكُمْ ۖ كَتَبَ رَبُّكُمْ عَلَىٰ نَفْسِهِ ٱلرَّحْمَةَ ۖ أَنَّهُۥ مَنْ عَمِلَ مِنكُمْ سُوٓءًۢا بِجَهَٰلَةٍۢ ثُمَّ تَابَ مِنۢ بَعْدِهِۦ وَأَصْلَحَ فَأَنَّهُۥ غَفُورٌۭ رَّحِيمٌۭ ﴿٥٤﴾
And when those come to you who believe in Our verses, say, "Peace be upon you. Your Lord has decreed upon Himself mercy: that any of you who does wrong out of ignorance and then repents after that and corrects himself - indeed, He is Forgiving and Merciful."
Allah has made mercy binding upon Himself.
Quran, Surah Az-Zumar 39:53
۞ قُلْ يَٰعِبَادِىَ ٱلَّذِينَ أَسْرَفُوا۟ عَلَىٰٓ أَنفُسِهِمْ لَا تَقْنَطُوا۟ مِن رَّحْمَةِ ٱللَّهِ ۚ إِنَّ ٱللَّهَ يَغْفِرُ ٱلذُّنُوبَ جَمِيعًا ۚ إِنَّهُۥ هُوَ ٱلْغَفُورُ ٱلرَّحِيمُ ﴿٥٣﴾
Say, "O My servants who have transgressed against themselves [by sinning], do not despair of the mercy of Allah. Indeed, Allah forgives all sins. Indeed, it is He who is the Forgiving, the Merciful."
Forbids despair and promises forgiveness to those who return.
Sahih Muslim 2752
Sahih... جعل الله الرحمة مائة جزء فأمسك عنده تسعة وتسعين ...
"Allah made mercy in a hundred parts; He kept ninety-nine and sent down one part to the earth."
Shows the scale of Allah's mercy.
Sahih al-Bukhari 5999
Sahih... لله أرحم بعباده من هذه بولدها ...
"Allah is more merciful to His servants than this woman is to her child."
Compares Allah's mercy with a mother's love.
Sahih al-Bukhari 3194
Sahih... كتب في كتابه فهو عنده فوق العرش إن رحمتي غلبت غضبي ...
"He wrote in His Book, which is with Him above the Throne: My mercy prevails over My wrath."
Allah's mercy outweighs His anger.
Where the ruling is recorded
- al-Aqida al-Tahawiyya, Section on hope and fear. Teaches that the believer lives between hope in Allah's mercy and fear of His punishment.
- Sharh al-Aqa'id al-Nasafiyya (al-Taftazani), Section on the attributes of Allah. Explains how attributes like mercy are affirmed without likeness to creation.
Checked by our team. For a more accurate answer to your own situation, consult a scholar. Quran translation by Sahih International. Hadith Arabic from the standard editions of the six books and the Muwatta, with gradings as recorded there; the English is our own rendering. Spotted a mistake? Tell us.