Using ΔE_P = mgΔh without tripping up

Every $\Delta E_P = mg\Delta h$ question wants one of three things:

1. the energy gained or lost (the usual one);
2. the height change, given the energy;
3. the mass, given the energy and the height.

Same formula, rearranged. The only real skill is deciding which quantity you already have.

The $h$ in the formula always carries a $\Delta$, and that matters.

A book on a $2.2\ \text{m}$ shelf moved down to a $1.5\ \text{m}$ shelf has changed height by $1.5 - 2.2 = -0.7\ \text{m}$. Its height above the floor is still $1.5\ \text{m}$, but the change is what stores or releases energy.

Choose a starting level, choose an ending level, subtract. It genuinely does not matter where you put zero — only differences are physical.

• Rising: $\Delta h$ is positive, so $\Delta E_P$ is positive — the store fills up.
• Falling: $\Delta h$ is negative, so $\Delta E_P$ is negative — the store empties.

A negative answer is not a mistake. It means energy left the gravitational store and went somewhere else (usually into kinetic energy, or into thermal energy if friction is involved).

If a question asks for "the energy released", give the size, without the minus sign.