The popular claim that a space heater "saves money" is only half true, and the wattage math shows exactly when it holds. A 1,500 W heater is a genuinely large load — the same order of magnitude as a hair dryer or a microwave, but running for hours instead of minutes. Whether it saves money depends entirely on zone heating: using the heater to warm only the room you occupy while turning the central thermostat down for the rest of the house.
Here is the trade-off in numbers. Suppose you drop your central heat by several degrees and that saves your furnace, say, $3.00 worth of energy over an evening. If you then run one 1,500 W heater for 6 hours to keep your occupied room comfortable, that heater uses 1.5 × 6 = 9 kWh, or about $1.53 at $0.17/kWh. Net result: you spend $1.53 to save $3.00, a real gain of roughly $1.47 that evening. The strategy wins because you are heating a few hundred square feet instead of the whole house.
But the math flips fast when you scale up. Run three 1,500 W heaters at once — a common temptation in a cold house — and you are drawing 4,500 W, or 27 kWh over those same 6 hours, about $4.59. Now you have spent more than the $3.00 the furnace would have cost, and you have likely tripped a breaker or two, because three 1,500 W heaters need three separate 15-amp circuits. Electric resistance heat is never cheaper than an efficient central furnace or a heat pump for warming an entire home; it only wins for spot-heating a single space.
Two other factors decide the outcome. First, your central heating fuel: zone heating with electric resistance almost always beats electric baseboard or an old electric furnace, but it may not beat a modern heat pump or cheap natural gas, since those deliver heat far more efficiently per dollar. Second, how well the room holds heat: a drafty room with single-pane windows bleeds warmth as fast as the heater adds it, forcing longer runtime and erasing the savings. Seal the drafts, close the door, heat only where you are, and use one heater on a thermostat that cycles off once warm — that is the specific recipe where a space heater lowers your bill rather than raising it.