AP Environmental Science Formula Sheet 2026 — All Calculations
AP Environmental Science (APES) is unique among AP science courses: all FRQs include at least one calculation question, and College Board does not provide a formula sheet. Every equation here appears directly on AP Enviro FRQs — memorize them all before exam day.
Population & Demographics
| Formula | Variables | When to use |
|---|---|---|
| Population Growth Rate (%) = [(Births + Immigration) − (Deaths + Emigration)] / Total Population × 100 | All values over same time period | Any problem asking for "growth rate" or "rate of natural increase" |
| Simplified: Growth Rate = (Birth Rate − Death Rate) per 1,000 × 100 | When immigration/emigration not given | Natural increase rate |
| Doubling Time = 70 / Growth Rate (%) | Rule of 70; growth rate as a percentage (e.g., 2%, not 0.02) | How long until population doubles at current growth rate |
| Population at time t = P₀ × (1 + r)ᵗ | P₀ = initial population, r = growth rate as decimal, t = years | Projecting future population size |
| Population Density = N / Area | N = number of individuals, area in km² or hectares | Density problems |
Rule of 70: At 2% growth, doubling time = 70/2 = 35 years. At 1% growth, doubling time = 70 years. This is one of the most tested APES calculations.
Energy & Resource Calculations
| Formula | Variables | When to use |
|---|---|---|
| EROEI = Energy Output / Energy Input | EROEI = energy return on energy invested; both in same units (joules, BTU, etc.) | Comparing energy sources; higher EROEI = more efficient |
| Net Energy = Energy Output − Energy Input | Actual usable energy after accounting for production costs | |
| Efficiency (%) = (Useful Energy Output / Total Energy Input) × 100 | Any problem about energy conversion efficiency | |
| Energy saved = Baseline use − Actual use | Conservation and efficiency scenarios | |
| Per capita consumption = Total consumption / Population | Comparing countries or time periods |
Ecological & Carbon Footprint
| Formula | Variables | When to use |
|---|---|---|
| I = P × A × T | I = environmental impact, P = population, A = affluence (GDP/capita), T = technology (impact per unit GDP) | IPAT equation — assessing total human impact |
| Carbon Footprint = Activity × Emission Factor | Activity in miles, kWh, etc.; emission factor in kg CO₂ per unit | Calculating CO₂ from transportation, electricity, etc. |
| NPP (Net Primary Productivity) = GPP − Respiration | GPP = gross primary productivity; NPP = energy available to consumers | Food chain efficiency problems |
| 10% Rule: Energy available at next trophic level = current level × 0.10 | Trophic efficiency problems |
10% Rule: If plants have 10,000 kcal, herbivores have ~1,000 kcal, carnivores ~100 kcal. This is tested as both a calculation and a concept.
Pollution & Chemistry
| Formula | Variables | When to use |
|---|---|---|
| pH = −log[H⁺] | [H⁺] = hydrogen ion concentration in mol/L | Calculating pH of acidic solutions |
| pOH = −log[OH⁻] | [OH⁻] = hydroxide ion concentration | Basic solutions |
| pH + pOH = 14 | At 25°C | Finding pH when pOH given (or vice versa) |
| pH change of 1 unit = 10× change in [H⁺] | Logarithmic scale | Comparing acidity: pH 4 is 10× more acidic than pH 5 |
| Concentration (ppm) = (mass of solute / mass of solution) × 10⁶ | ppm = parts per million | Pollution concentration problems |
| Dilution: C₁V₁ = C₂V₂ | C = concentration, V = volume | Calculating pollutant concentration after dilution |
Soil, Water & Agriculture
| Formula | Variables | When to use |
|---|---|---|
| Soil Erosion Rate (tons/acre/yr) — given in problems | T value = tolerable soil loss rate (~1–5 tons/acre/yr) | Compare actual erosion to T value |
| Water footprint = Volume of water / unit of product | L per kg, gallons per pound, etc. | Comparing food or product water intensity |
| Crop yield change (%) = (New yield − Old yield) / Old yield × 100 | Green Revolution, GMO, fertilizer effect problems |
Unit Conversions You Must Know
| Conversion | Value |
|---|---|
| 1 kilowatt-hour (kWh) | 3.6 × 10⁶ joules (3.6 MJ) |
| 1 metric ton CO₂ | 1,000 kg CO₂ |
| 1 hectare | 10,000 m² ≈ 2.47 acres |
| 1 BTU | ≈ 1,055 joules |
| 1 calorie (food) | 1 kilocalorie = 4,184 joules |
Calculation Types on the APES FRQ
College Board FRQ data (2019–2025) shows these calculation types appear most frequently:
- Population growth rate and doubling time — appears on ~90% of exams
- Energy/EROEI calculations — appears on ~70% of exams
- Percent change — appears on ~80% of exams (deforestation rate, emission reduction, etc.)
- pH and acid rain — appears on ~50% of exams
- 10% rule / trophic efficiency — appears on ~60% of exams
FRQ Calculation Strategy
- Write the formula first — you earn a point for the correct formula even with arithmetic errors
- Show all units — cancel units carefully; if your final unit doesn't match the question's expected unit, you have the wrong formula
- State the formula name — "Using the Rule of 70: doubling time = 70 / 2.5% = 28 years"
- Use scientific notation for very large/small numbers; don't round prematurely
Calculate your predicted AP Enviro score
AP Environmental Science Score Calculator →AP Environmental Science Score Cutoffs (2026)
| AP Score | Composite Range |
|---|---|
| 5 | 71–100 |
| 4 | 56–70 |
| 3 | 40–55 |
| 2 | 26–39 |
| 1 | 0–25 |
Frequently Asked Questions
Does AP Environmental Science provide a formula sheet?
No. APES does not provide any formula sheet during the exam. All formulas must be memorized. The Rule of 70, EROEI, population growth rate, and the 10% rule are the highest-priority equations to memorize.
How many calculation questions are on the APES FRQ?
Every AP Environmental Science FRQ typically includes at least one calculation sub-question. Across the three FRQ questions (one of which is the "design an investigation" type), you should expect 2–4 numerical calculations requiring formula recall.