Jesus's atonement equivalent to sinners' punishments

Since you did not ask for the doctrinal position from any particular denomination, I will answer this question from a biblical perspective. The Bible does not explain how Christ's sacrifice was sufficient, but it does make clear that it was sufficient. For instance:

Is 53:10-11 (NASB)

But the Lord was pleased
To crush Him, putting Him to grief;
If He would render Himself as a guilt offering,
He will see His offspring,
He will prolong His days,
And the good pleasure of the Lord will prosper in His hand.
As a result of the anguish of His soul,
He will see it and be satisfied;
By His knowledge the Righteous One,
My Servant, will justify the many,
As He will bear their iniquities.

Since the Bible is not clear as to why Jesus' sacrifice was sufficient, believing that it was sufficient is a matter of faith. There are some helpful explanations which have been given, but they are speculative:

• Jesus was Innocent - When an innocent person accepts the punishment for someone else, it softens the wrath of the Judge and the sentenced may be reduced.
• Jesus Became Sin - According to 2 Cor 5:21, Jesus became sin for us. Many people interpret this to mean that Jesus became sinful and was spiritually separated from His Father. He experienced spiritual death and a loss of communion with the Father. This change is beyond any specific punishments which might be experienced.
• Jesus is Divine - As a member of the Godhead, Jesus' sacrifice is more significant than that of any mere created being.

Note: All Scripture is quoted from the King James version.

The punishment for sin is not being sent to Hell; the punishment for sin is death.

Genesis 2:17 But of the tree of the knowledge of good and evil, thou shalt not eat of it: for in the day that thou eatest thereof thou shalt surely die.

That having been said there are some Denominations who believe that Jesus did indeed spend those three days in Hell, preaching to those who had died before his crucifixion.

So if the punishment for sin is death, then what is death?

Very often we are told that death is eternal separation from God, and to their credit I also believe that eternal separation from God is a large part of death, but it is not all of what death means.

The Revelation tells us that there are two deaths:

Revelation 1:18 I am he that liveth, and was dead; and, behold, I am alive for evermore, Amen; and have the keys of hell and of death.

Revelation 20:14 And death and hell were cast into the lake of fire. This is the second death.

In the Revelation 1:18 Jesus statement that he has the keys of Hell and Death, tells us that whether we suffer Hell or Death is dependent on him. Or in other words he and he alone is the one who will determine where we will spend our eternity. Part of that eternity can be spent in either of two places.

Those who have rejected salvation will initially be sent to Hell, and later cast into the lake of fire.

Matthew 10:28 And fear not them which kill the body, but are not able to kill the soul: but rather fear him which is able to destroy both soul and body in hell.

This tells me that this is the first death, and that at physical death both body and soul will be sent to Hell to await the Great white throne judgment.

Revelation 20:11 And I saw a great white throne, and him that sat on it, from whose face the earth and the heaven fled away; and there was found no place for them.

But neither Hell or death are eternal as is said in Revelation 20:14.

And death and hell were cast into the lake of fire. This is the second death.

and those who had been in Hell will now be cast into the lake of fire.

Revelation 20:13 And the sea gave up the dead which were in it; and death and hell delivered up the dead which were in them: and they were judged every man according to their works.

Revelation 20:15 And whosoever was not found written in the book of life was cast into the lake of fire.

Since death and Hell were cast into the lake of fire those cast into the lake of fire will not ever escape eternity by dying but will suffer torment for all eternity.

Revelation 20:10 And the devil that deceived them was cast into the lake of fire and brimstone, where the beast and the false prophet are, and shall be tormented day and night for ever and ever.