Projection is a breath problem, not a volume problem
The people who cannot be heard at the back are rarely speaking too quietly. They are speaking on the wrong air, and shouting makes it worse.

The short answer
If people at the back of the room cannot hear you, turning up the volume is the wrong instruction. Loudness produced by pushing harder at the throat gets you about twenty per cent more sound, a tighter voice, and a sore larynx by the afternoon. Loudness produced by more air under the voice gets you a sound that travels, and costs you nothing.
Power, in the four-dial sense, is not “be louder.” It is having enough breath behind the voice that volume becomes a choice rather than an effort. Get that right and the range you can move through, quiet to loud, roughly doubles.
Why pushing does not work
The voice is a wind instrument. Air comes up from the lungs, the vocal folds convert it into sound, the mouth and throat shape it. Volume is a function of how much air is moving and how efficiently it becomes sound.
When someone is told to speak up and has no more air available, they do the only thing left: they squeeze. The throat tightens to force more pressure out of a small supply. That produces a sound that is louder at the source and worse at the back of the room, because it is thinner, harsher and pitched slightly higher, and because the effort audibly reads as strain.
I hear this constantly in first sessions with people who present in large rooms. They have been told to project for years. What they have learned is to shout politely.
What is actually going wrong
Almost always, the breath is high and small.
In ordinary conversation you need very little air, and most adults breathe in the upper chest all day without any cost. Put those same people in front of eighty faces and the breathing goes higher and shallower still, because that is what adrenaline does. Now they are trying to fill a room on a teacup of air.
The tell is the end of the sentence. Listen to a nervous speaker and the first half of each sentence is fine and the last three words fall off a cliff. That is not a confidence wobble. It is running out of air and finishing the thought on the dregs, which is also why the pitch drops and the words blur together at exactly the point where the actual content usually lives.
The change that matters
Breathe lower and refill more often. That is genuinely most of it.
Lower means the movement you can feel is around the bottom of the ribs and the stomach, not the shoulders. Put a hand flat on your stomach: on the in-breath it should move outward. If your shoulders rise instead, the air is going to the top of the lungs, which holds the least and empties the fastest.
More often means taking air at punctuation deliberately, rather than waiting until you need it. Speakers who refill only in emergencies spend most of every sentence on a falling supply. Speakers who top up at every full stop never get near the bottom, and never sound like they are labouring.
Posture is the unglamorous third piece. Feet under you, weight even, knees not locked, shoulders down and back and not hunched forward over a lectern. A collapsed rib cage cannot take a full breath. I would rather a client fixed how they stand than practised any exercise in this article.
How to build the capacity
Two things, done badly and regularly, beat anything done well and once.
Breathe in through the nose for a slow count of four, feeling the ribs widen sideways rather than the chest lift. Then let it out on a steady whispered ah for a count of four. Repeat five or six times. The point is not the counts, it is noticing where the movement happens.
Then the same breath, but count out loud on the way out, and go for as long as one breath lasts you comfortably. Do it against a wall at the far side of the room and aim the sound at the wall. Most people find they are somewhere in the low teens at first and can add several counts within a fortnight. That is not a party trick. It is the reserve that stops your sentences dying at the end.
Do these sitting at a desk, not while panicking before a talk. A physical skill you can only reach in calm conditions is not a skill you have yet.
Quiet is a power setting too
The half of this that nobody teaches: going quieter is the strongest move available to a speaker who has established that they can fill the room.
Dropping the volume for a sentence makes an audience lean in, physically. It is the clearest way to mark something as important without any of the theatre that emphasis usually involves. It only works if the consonants stay energetic, though. Quiet speech with lazy articulation is just inaudible speech, and the room will assume you have lost your nerve rather than made a choice.
So the real skill in power is not maximum output. It is the size of the gap between your loudest and your quietest while both remain completely clear. A speaker with a wide gap can shape twenty minutes. A speaker with a narrow gap has one setting, and by minute six the room has stopped noticing it.
What this does not fix
Two honest limits.
A room with bad acoustics or no PA will beat good technique. If you are handed a microphone, take it, and then stop projecting — the commonest mistake with a mic is continuing to push, which overloads it and sounds worse than not using one.
And if your voice tires, goes hoarse, or gives out after moderate use, that is not a technique question and I am not the right person. Persistent hoarseness lasting more than three weeks warrants a GP referral to an ENT clinic. I will say so on the first call rather than sell you sessions.
Where this sits
Power is the third dial I would work on, after pause and pace, for the simple reason that breath needs somewhere to happen. A speaker with no gaps has nowhere to take air, so the projection work has nothing to stand on. The full four-dial framework sets out the order.
Breath under adrenaline is a related and slightly different problem, covered in public speaking fear is a breathing problem. One-to-one work on voice and breath runs through my elocution lessons; room craft and delivery through the public speaking course.
Common questions
Is projection the same as speaking loudly?
No. Projection is directing a supported sound to a distance. Loudness is amplitude at the source. A projected voice at moderate volume carries further and more clearly than a shouted one, because the strain that comes with shouting narrows the sound.
Will breathing exercises make my voice deeper?
Slightly, and indirectly. Removing throat tension usually lets the voice settle to its natural resting pitch, which is often a little lower than where a tense speaker has been sitting. It will not change the instrument, only stop you fighting it.
How long before it is audible to other people?
In my experience, two to three weeks of short daily practice is when clients start reporting that people stopped asking them to repeat things. The change in a recording is usually obvious before the change in sensation is.
Do I still need this if I always have a microphone?
Less, but not none. A microphone amplifies whatever it is given, including strain and dying sentence endings. Breath support is what makes the end of a sentence carry, and no amount of gain fixes that.