AP Environmental Science · Reference

AP Environmental Science formula sheet the equations you actually need.

Here is the AP Environmental Science formula sheet — also called the equation sheet — covering the population, energy, pollution, and percent-change math the exam expects. The good news: APES now provides a reference and equation sheet and permits a calculator, so the real skill is knowing which formula a question calls for and showing your setup.

Updated June 2026Part of AP Environmental Science Review

Does the AP Environmental Science exam provide an equation sheet?

Yes. The College Board provides reference materials — an equation sheet and reference tables — for AP Environmental Science, and, in a recent change, an approved calculator is now permitted on the exam. For years APES students had to do every calculation by hand from memory; that is no longer the case.

What has not changed is that the free response asks you to set up the math and show your work, so knowing which equation applies still matters. The list below is grouped by topic so each formula sits next to where you use it.

The AP Environmental Science formula sheet, by topic

The math that actually shows up, with a plain-language note on when to use it.

Populations & growth

Rule of 70: doubling time (yrs) = 70 / growth rate (%)

The classic APES shortcut for exponential growth.

Population growth rate (%) = [(births + immigration) − (deaths + emigration)] / N × 100

The full change in a population.

Exponential growth: N = N₀e^rt

Future population size at growth rate r.

Percent change & per-capita

Percent change = [(new − old) / old] × 100

Used everywhere — resource use, emissions, land cover.

Per-capita value = total / population

Turns a national total into a per-person figure.

Energy & power

Energy = power × time

e.g. kilowatt-hours = kilowatts × hours.

Efficiency (%) = (useful output / input) × 100

How much energy actually does useful work.

Metric prefixes: kilo (10³), mega (10⁶), giga (10⁹)

You will convert between these constantly.

Pollution & decay

Half-life: remaining = initial × (½)^{t / half-life}

For radioactive waste and the breakdown of pollutants.

Concentration (ppm) = (parts pollutant / parts total) × 10⁶

Reading and comparing pollutant levels.

The skill that matters most

Dimensional analysis (unit conversion)

Most APES math is really careful unit conversion — line the units up so they cancel, and show every step.

How to use this formula sheet

Because a reference sheet and calculator are provided, memorizing every equation matters less than knowing when each one applies and setting the calculation up cleanly. Practice picking the right formula from a word problem, and always write out your units — unit errors, not arithmetic, cost the most points.

For a faster, concept-first version that pairs each unit with its key idea and the mistake to avoid, use our APES cheat sheet, work full problems against the rubric with the FRQ guide, and the score calculator turns a practice raw score into a 1–5.

Frequently asked questions

Quick answers — written by humans, not a chatbot.

Does AP Environmental Science provide an equation sheet?

Yes. The College Board provides reference materials — an equation sheet and reference tables — and, in a recent change, a calculator is now permitted on the exam.

Is a calculator allowed on AP Environmental Science?

Yes. An approved four-function, scientific, or graphing calculator is now permitted on the whole exam.

What math is on the AP Environmental Science exam?

Population growth and the rule of 70, percent change, energy and efficiency, half-life, and unit conversions — usually straightforward arithmetic, but you must show the setup.

Do I need to memorize formulas for AP Environmental Science?

Less than before, since a reference sheet is provided, but you still need to know which formula a question calls for and how to set up the calculation.

What is the rule of 70 in APES?

A shortcut for doubling time: divide 70 by the percent growth rate. A population growing 2% a year doubles in about 35 years.