Your children can be restless and unable to calm down when they are just full of energy. They are only being very active. It is really hard to sit still, stand still, or be still. Their problem is not stress, it is having to be calm and quiet.
School and the dinner table are good examples. The only stress is adults who expect them to quit fooling around. Your children are just being children. The adults are the ones with the stress.
When restlessness and trouble calming down are because of stress, it does not feel good. Your young person is having thoughts and feelings keeping him upset. He is confused and feels afraid, angry, and frustrated at the same time. He cannot manage these thoughts and feelings very well and is up-tight and uneasy.
If this sign is present for your child, think about whether he has a problem or if perhaps you are simply having difficulty coping with his energy and normal behavior. If the issue actually reflects your stress, share your problem with him. You might say, "I want to talk with you about slowing down and settling down a little, especially at dinner and when we're having quiet time in the evening. You're too noisy; and I find it hard to handle."
If you think your child may be restless and having trouble calming down because of stress, offer to talk with him about whatever is bothering him, assure him you want to try to help him if he wants, and then give him a little more space. You may simply need to be more patient and tolerant. It also helps to understand your children probably handle the big stresses in their lives fairly well; and you likely know what those are. It is the little stresses that build and accumulate for your children, as they do for you. Understanding this helps you to be more patient, to not expect your child to specifically know what is bothering him, and to give him more personal and emotional freedom to work through his unique stresses.
You might say, "I can tell you have a lot on your mind. I'll give you as much time and space as you need to work it out. If you want to talk, I'm here for you."
If he is not noticeably more relaxed in a day or so, become somewhat more insistent. You might say, "Whatever you are struggling with seems like a big problem for you. I can't tell whether you are winning or if whatever is bothering you is winning. It's time to talk. Let me help. I know the two of us can handle any problem better than either of us by ourselves. Can we talk?"
If he refuses to talk, keep trying, not right then but from time-to-time and at least once a day. Do not become frustrated and up-tight just because he does not talk to you. Helping your youngster with stress can be stressful. Nonetheless, model good stress management behavior.