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AK vs huge 4bet - how much equity needed to jam?

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AK vs huge 4bet - how much equity needed to jam?

Blinds: $0.10/$0.25 (6 Players) BN: $40.42
SB: $28.86 (Hero)
BB: $19.66
UTG: $34.13
MP: $12.61
CO: $23.04
Preflop ($0.35) Hero is SB with K A
2 folds, CO raises to $0.75, BN folds, Hero raises to $2.50, BB folds, CO raises to $7.75, Hero raises to $28.86 and is all in, CO calls $15.29 and is all in

This hand is posted mainly as a calculation exercise.
Can someone tell me how to calculate how much equity I need when I shove over his 3bet if I give him a range that only consists of QQ+ (for calculation purposes).

I am risking around $20 to win the full pot $52 = 38% equity needed.
I have 31% vs QQ+ so this is a bad shove? Is my calculation correct?

tx

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