If you roll to the center of your mattress and sink, you have a problem with a sagging mattress. When looking for solutions, using plywood can improve your sleep in the short term. It's not the best solution, but plywood under the mattress is a decent temporary fix.
Mattresses sag for two reasons: insufficient support from beneath or a breakdown in their internal support structures. If you don't use a box spring beneath your mattress, it could sag simply from its own weight. It is designed to be most comfortable when resting on a foundation. If you do have a foundation for your mattress, it sags because it is old. Over time, your sleeping weight exerts enough pressure on the interior of the mattress to weaken the materials there, leading to soft spots and sagging.
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Plywood can help with a sagging mattress. If the issue is lack of support, use plywood to give the mattress a firmer base. Lay a sheet of plywood down on the slats of your bed frame, and place the mattress on top of it. It will support the mattress from beneath, stopping it from sagging. If the issue is an older mattress, plywood can give you a temporary solution. Cut a piece of plywood to match the size and shape of the sagging area, and place it under the mattress in the soft spot. It will push up on the mattress in the problem area, making it feel firmer and more like the rest of the mattress.
Using plywood under a sagging mattress does have some drawbacks. Because the bottom of the mattress rests flat against the wood, less air circulates around it, which increases the risk of mildew growth on the bottom of your mattress, especially if you live in a humid climate. Mildew will ruin your mattress. If your mattress is old, it will continue to sag and get softer over time. The plywood helps temporarily, but as time goes on, it won't be enough to make the mattress comfortable.
You can use plywood as a short-term solution for a sagging mattress while you look for a long-term fix, like purchasing a box spring or a new mattress. Rotate or flip a sagging older mattress, which can expose you to unused portions of the mattress with better internal support and can give you a firmer place to sleep without needing to use the plywood.