Lean Performance Lab LPL

Should I train when I am sore?

Usually yes: soreness is not damage you need to wait out, though a muscle that is still weak or painful to move deserves another day.
Evidence Moderate Reviewed Sources 2

Most soreness comes from doing something new, or more of it than usual. Repeat the same session and it shrinks, which is why week three of a program hurts far less than week one even though you are lifting more.

Train the sore muscle again when it can produce force normally. If your warm-up sets feel heavier than usual, drop the load rather than skipping the session. Hold off only when a specific spot hurts sharply, when the pain is in a joint rather than a muscle, or when a muscle still cannot move through its full range.

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Sources 2