You can definitely do a chest and tricep workout at home if you know the right exercises to include in your routine. Of course, your equipment availability makes a big difference to your exercise selection, so you'll naturally have more training variety at your disposal if you've got gear like bands and dumbbells.
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- Chest and tricep workout without weights
A muscle-building chest and tricep workout at home
This chest and triceps home workout will stimulate both muscle growth and strength development by training your chest and tris from different angles and with a variety of rep ranges.
The routine uses dumbbell, body weight, and band exercises as these movements are more accessible than barbell, cable, and machine exercises.
As I outline this at home chest and triceps workout, I'll include recommendations for substitute exercises in case you don't have the equipment to perform a particular movement.
Rest 1-2 minutes between exercises. Where there's a superset, perform both exercises in the superset and then rest. 
Exercise 1: Dumbbell bench press — 3-5 sets of 8-12 reps
You'll need a bench and weights to do this mass-building chest and tricep exercise. However, dumbbells and a basic weight bench are pretty affordable these days, and they'll dramatically increase your exercise possibilities, so they’re definitely worth having.
The key with the dumbbell bench press is to lower the weights down and then slightly out so that you can maximally stretch your pecs. Once you feel a deep chest stretch, you want to extend your elbows and aggressively push your hands into the dumbbell handles to press the weights back up.
If you've got some dumbbells but no weight bench, then you do a floor press instead, which is a more triceps-dominant exercise.
If you've got bands but no weights or a bench, then you can use a door anchor to essentially create a high pulley station, from which you can do a resistance band chest press.
Exercise 2A: Wide-grip push-ups — 3-5 sets of 15-30 reps
Wide-grip push-ups are the first exercise in this chest-pumping superset, and they're one of the most underrated movements for sculpting well-built pecs.
By using a wider hand position, your chest will naturally receive a deeper eccentric stretch, which leads to a more potent hypertrophic stimulus and ultimately more muscle growth.
If you're already really strong, then you can make wide-grip push-ups harder by hooking a band around your back and then around your hands. This modification will force your pecs to contract harder at the top of the rep, which will result in a stronger muscle pump.
Exercise 2B: Resistance band flys — 3-5 sets of 15-20 reps
If you've got a pair of weights handy, then you can certainly do dumbbell flys. However, I like resistance band flys because they're the exact opposite of a dumbbell fly.
Rather than emphasizing the stretch portion of the rep, banded flys elicit a massive peak contraction in your pecs.
Considering that you've already put your chest under a big weighted stretch with bench presses and push-ups, it's beneficial to maximally contract your pecs by bringing your arms all the way across your body with a banded fly.
There are multiple ways to do a band fly, but my favorite method for getting the best pump and contraction is to do a single-arm resistance band chest fly, where you anchor your bands to the side of your door at shoulder height and then perform a simple fly motion where you bring your upper arm across your body.
Exercise 3: Dumbbell overhead extension — 3-5 sets of 10-15 reps
No chest and tricep home workout is complete without an overhead extension. This is because, unlike pushdowns and presses, overhead extensions train the long head of the triceps, which is bigger than both the medial and lateral heads of the triceps combined.
Therefore, if you want to build bigger arms, then you have to make the long head of the triceps a real priority in your training. In order to do that, you need to perform elbow extension—which is the main function of the triceps—while your shoulders are in flexion.
In practice, this often means doing an overhead extension. But if you have access to a weight bench, then you can also get identical results from doing a lying tricep extension because the shoulder position (which is what counts for long head activation) is exactly the same.
Just make sure to use a full range of motion to maximize your results. You want to lower the dumbbell as far behind your neck as you comfortably can so that you can properly stretch your triceps and break down the muscle fibers. After that, you want to achieve full elbow extension by straightening your arms at the top of every rep. Locking out the elbows is, after all, the main job of the triceps brachii.
Exercise 4A: Close-grip push-ups — 3-5 sets of 10-20 reps
Close-grip push-ups are the penultimate exercise in this chest and triceps home workout and one that many weight lifters often neglect.
The trick to getting the most from this movement is to keep your elbows close to your sides as you lower your chest to the ground and then push yourself back up. This reduces the ability of your pecs to produce force, which in turn makes your triceps work harder.
You also want to use a slightly narrower hand position than usual. However, this is less important than the position of your elbows, so there's no need to use mega-close hand spacing if it puts pressure on your wrists.
As for whether you should train chest and triceps or chest and biceps together, it depends on the rest of your program. But since push-ups already train your tris, it can often make sense to do chest and triceps in the same session.
Exercise 4B: Tricep dips — 3-5 sets of 20-40 reps
Tricep dips are a must-do exercise when you're performing an at home chest and triceps workout because you can do them almost anywhere, whether that's on the edge of a bench, a chair, the sofa, or your bed. 
Additionally, dips are also ideal for finishing off your triceps to make sure that any remaining muscle fibers get recruited. In this regard, when they're paired alongside close-grip push-ups, dips are an even more potent muscle-building tool.
You can also make tricep dips harder by either wearing a weighted vest or by raising your legs on another chair/bench and then putting weight plates on your outstretched legs.
See Also: How to get big triceps at home
How can you create a good chest and triceps workout at home?
If you have some basic equipment, then doing your chest and tricep workout at home makes a lot of sense because you really don't need any fancy machines to build your body.
If you have dumbbells, a bench, and some bands, then you can get a gym-quality workout in your living room, bedroom, or garage.
Of course, this equipment is optional, but such fitness gear will give you way more workout possibilities and will enable you to train your chest and tris for different angles.
So, what makes a good home chest and triceps workout?
At a minimum, you need to do some kind of push-up or chest press to give your pecs the fiber-tearing tension that they need to grow.
Additionally, you need to do some kind of overhead extension or lying extension to train your triceps because bench presses, push-ups, and dips don't work the long head of the triceps very well.
If your bench adjusts, then you can also do incline presses to hone in your upper chest (regular bench presses and even push-ups also work the upper chest, but to a lesser degree).
Conclusion: Should you do an at home chest and triceps workout or not?
Doing your chest and triceps workout at home is a great idea because you'll likely have fewer distractions when you're training by yourself.
Also, working out will seem like less of a chore when you don't have to commute to the gym.
Best of all, you won't need to wait for any equipment, which means that you can maintain your flow and get the best possible at home chest and triceps workout.
- Roberts, A. C. (2022). What Is a Superset and Why Should I Do It? Men’s Journal. https://www.mensjournal.com/health-fitness/what-superset-and-why-should-i-do-it/
- Mansour, S. (2021, April 23). How to do tricep dips: Tone your arms for summer - TODAY. TODAY.Com. https://www.today.com/health/how-do-tricep-dips-tone-your-arms-summer-today-t216006