"Deltoids" is the anatomical name for your shoulder muscles. Typical gym-based exercises that work the deltoids include dumbbell or barbell shoulder presses and machine shoulder presses. While you may not be able to replicate these exactly when training at home, there are plenty of other moves you can do that work the deltoids and can be useful for building strength and size.
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The Humble Pushup
Pushups are easy to overlook as a strength-building exercise, but they should be a key move in your home workout. Regular pushups hit your shoulder muscles, along with your chest muscles and triceps, but LA-based strength coach Anthony Yeung suggests trying different pushup variations to hit your shoulders harder. These include T-pushups, where you raise an arm off the floor and twist to the side after each rep; pushups with one arm off the ground; and pushups with a hand on a medicine ball.
In the gym, overhead moves would likely make up the majority of your shoulder workout. To replicate these at home, trainer Joe DiStefano recommends elevated pushups with your feet on a stair, as in a flight of stairs. Start on the lowest stair and gradually raise your feet higher as you get more confident. Additionally, you can make pushups more shoulder-dominant by bringing your hands closer toward your feet and raising your butt in the air, which takes some of the stress off the pecs and transfers it to the deltoids.
Isometric exercises are those that involve holding a position and are the easiest way to replicate dumbbell shoulder moves at home without equipment. To perform isometric lateral raises, stand side-on to a wall with your arm hanging down. If you're working your right side first, the wall should be on your right, with your shoulder and the back of your hand pressed against the wall. Push your hand into the wall as if you were trying to lift it out to the side. Push as hard as you can for five to 20 seconds, then switch sides. You can also try this standing a little further away from the wall.
Bring on the Bands
Even if you can't construct a whole gym at home, you can make your training a little more interesting by introducing equipment such as bands. Bands make a fine substitute for dumbbells on lateral raises, front raises and shoulder presses. The American Academy of Orthopaedic Surgeons suggests using bands for a home deltoid rehab workout and including internal and external rotations, as well as rows with the band attached to a door handle. Whether or not you have a deltoid injury, these would make a good addition to your workout or your warm-up.
Working Out the Warm-Up
Before starting your deltoid workout, add in a warm-up. If you have bands, use those to warm up, with just a little resistance applied. If not, then perform five to 10 minutes of light cardiovascular work, along with some shoulder mobility moves. These could include arm swings -- rotating your arms in a circular motion both forward and backward -- as well as some light resistance exercises, such as knee pushups and a little stretching.