IB Diploma Programme Environmental Systems and Societies (SL)
All 8 ESS topics, every key calculation (NPP, ecological footprint, Simpson's index, Lincoln index, biotic index), statistical methods and the Individual Investigation — your complete transdisciplinary ESS reference for 2026.
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Aligned with the latest 2026 syllabus and board specifications. This sheet is prepared to match your exam board’s official specifications for the 2026 exam series.
IB Diploma Programme Environmental Systems and Societies is a transdisciplinary SL course bridging Group 3 and Group 4. It rewards systems thinking, value-system awareness AND quantitative analysis. This formula sheet brings together every topic, calculation and method you need for Paper 1, Paper 2 and the Individual Investigation in 2026.
All 8 ESS topics from Foundations through to Resources
Every assessed calculation — NPP, ecological footprint, Simpson's, Lincoln
Statistical methods: Spearman's, t-test, chi-squared, kite diagrams
Individual Investigation structure (10 hours, 1,500–2,250 words, 25%)
Establishes systems thinking and the role of values in environmental decisions.
A worldview that shapes how individuals/societies evaluate environmental issues.
Ecocentric
Nature-centred; intrinsic value of ecosystems; minimum disturbance; deep ecology. Anthropocentric
People-centred; sustainable use of resources; population control, regulation, education. Technocentric
Technology can solve environmental problems; pro-growth; scientific research and innovation. ESS treats the environment as systems with inputs, outputs, storages and flows.
Open system
Exchanges matter AND energy with surroundings (most ecosystems). Closed system
Exchanges energy but NOT matter (e.g. Earth as a whole, mesocosms). Isolated system
Exchanges neither matter nor energy (theoretical only). Transfer
Matter/energy moves through a system without changing form (e.g. water flowing in a river). Transformation
Matter/energy changes form/state (e.g. photosynthesis, evaporation). Use of natural capital so that natural income is maintained for future generations; quantified using natural capital, natural income and ecological footprint. Quantitative ecology — productivity, diversity and population estimates.
Energy fixed by producers and passed through trophic levels.
GPP
Gross Primary Productivity = total energy fixed by producers (per area per time). NPP
NPP = GPP − R (R = energy lost in respiration). Energy available to next trophic level. Trophic transfer
≈ 10% rule — only ~10% of energy at one trophic level becomes biomass at the next. Measures species diversity in a community.
Formula
D = 1 − Σ (n / N)² where n = individuals of one species, N = total individuals. Higher D ≈ greater diversity (max value 1). Always quote units of habitat and sample size.
Estimates population size of mobile animals.
Formula
N = (n₁ × n₂) / m₂ where n₁ = first sample, n₂ = second sample, m₂ = marked recaptured. Assumes no births/deaths/migration between samples and that marking does not affect capture.
Producers → primary consumers → secondary → tertiary → top consumers; pyramids of numbers, biomass and productivity (productivity always upright). Succession: pioneer → seral stages → climax community; primary vs secondary succession. Species diversity · habitat diversity · genetic diversity. Habitat loss/fragmentation, overexploitation, invasive species, pollution, climate change, disease. In-situ
National parks, nature reserves, community conservation — protects whole habitat. Ex-situ
Zoos, captive breeding, seed banks, botanic gardens — last-resort or supportive. IUCN Red List categories: EX, EW, CR, EN, VU, NT, LC, DD.
Storages: oceans, ice caps, groundwater, rivers/lakes, atmosphere, biota. Flows: evaporation, transpiration, precipitation, infiltration, runoff. Cause
Nutrient enrichment (mainly N, P) from fertiliser runoff/sewage → algal bloom → algae die → decomposers raise BOD → O₂ falls → fish kill. BOD
Biochemical Oxygen Demand — mass of O₂ needed by decomposers per volume of water; high BOD = polluted water. CO₂ + H₂O ⇌ H₂CO₃ ⇌ H⁺ + HCO₃⁻; lower ocean pH reduces carbonate availability for shell/coral formation. Formula
MSY = (½ × carrying capacity × intrinsic growth rate) — largest catch that can be removed indefinitely without depleting the stock. Inputs: organic matter, weathered parent material, water, air. Storages: humus, mineral particles, soil organisms. Outputs: leaching, erosion, uptake by plants. Soil texture
Sandy (free-draining, low nutrients) · clay (waterlogged, high nutrients) · loam (balanced — best for agriculture). Use the soil texture triangle to classify by % sand/silt/clay.
Causes: deforestation, overgrazing, monoculture, irrigation (salinisation), urbanisation. Conservation: terracing, contour ploughing, cover crops, agroforestry. N₂ ~78% · O₂ ~21% · Ar ~0.9% · CO₂ ~0.04% (rising). Layers: troposphere → stratosphere (ozone) → mesosphere → thermosphere. Stratospheric ozone
O₂ + UV → 2O · O + O₂ → O₃; depleted by CFCs releasing Cl radicals (Montreal Protocol 1987). Photochemical smog
NOₓ + VOCs + sunlight → tropospheric O₃ — worsened in temperature inversions; urban heat island effect. Acid deposition
SO₂ + NOₓ → H₂SO₄ / HNO₃; pH < 5.6; damages forests, lakes, buildings. Solar SW radiation absorbed by Earth → re-emitted as LW IR → trapped by GHGs (CO₂, CH₄, N₂O, water vapour, halocarbons) → warming. Radiative forcing
Net change in energy balance (W m⁻²); positive = warming, negative = cooling. Mitigation
Reducing causes — renewables, carbon capture, afforestation, energy efficiency, dietary change. Adaptation
Reducing impacts — sea defences, drought-resistant crops, flood-resilient infrastructure, migration. IPCC reports synthesise current science; UNFCCC/COP processes negotiate global response.
Compare: fossil fuels (high energy density, high CO₂) · nuclear (low CO₂, waste/safety) · solar/wind/hydro/geothermal/biomass — by economic, ecological, cultural and political criteria. Land area required to sustain a population.
Formula
EF = (population × per capita resource use) / (yield + waste assimilation capacity). Compare EF with biocapacity — overshoot occurs when EF > biocapacity. Units: global hectares per person.
Compare terrestrial vs aquatic; intensive vs subsistence; LEDC vs MEDC; consider energy efficiency, water use, soil health, biodiversity. Reduce → Reuse → Recycle (then Recover energy → Dispose). Hierarchy of waste management; circular vs linear economy. CBR / CDR
Crude Birth/Death Rate per 1,000 per year. Natural increase rate (%) = (CBR − CDR) / 10. DTM
Demographic Transition Model — 5 stages from high CBR/CDR to low CBR/CDR. Chosen for the Individual Investigation and Paper 2 data analysis.
Spearman's rank correlation (rₛ)
Tests strength of monotonic relationship between two ranked variables. Range −1 to +1. Student's t-test
Compares means of two normally distributed samples. Critical t at p = 0.05 with df = n₁ + n₂ − 2. Chi-squared (χ²)
χ² = Σ ((O − E)² / E); compares observed vs expected frequencies; df = (rows − 1)(cols − 1). Random (random number generator) · systematic (e.g. every 10 m along a transect) · stratified (samples proportional to subgroup) · belt/line transect for gradients. Line / scatter graphs (continuous data + relationship) · bar charts (categorical) · kite diagrams (abundance along a transect) · pyramids of biomass / productivity. Use indicator species to infer pollution (e.g. Trent biotic index, Saprobien index for freshwater quality). Worth 25% of the final grade. Plan early — data collection cannot be rushed.
10 hours of work · 1,500–2,250 words · practical-based investigation linking environmental and societal aspects. Identifying the context · Planning · Results, analysis and conclusion · Discussion and evaluation · Applications. Sharply focused research question · justified methodology · processed data with appropriate statistics · evaluation of method limitations · realistic 'so what' application section. ESS IAs must engage BOTH the environmental and societal dimensions — not just one.
Boost your Cambridge exam confidence with these proven study strategies from our tutoring experts.
Simpson's index, Lincoln index, NPP = GPP − R, ecological footprint, MSY and natural increase rate appear repeatedly. Practise each on past-paper data.
Paper 2 examiners reward answers that explicitly compare ecocentric, anthropocentric and technocentric viewpoints — name them and justify which is most appropriate.
Decide on your statistical test BEFORE you collect data — it dictates how many replicates and what variables you need to record.
Anchor every topic in a named example (e.g. Aral Sea for unsustainable irrigation, Easter Island for resource collapse, Yellowstone for in-situ conservation).
Quick answers about this free PDF and how to use it for exam revision and active recall.
Yes. This Tutopiya formula sheet is free to use and you can download it as a PDF from this page for offline revision. There is no payment or account required for the PDF download.
This page groups key Environmental Systems and Societies formulas in one place for revision. Master IB Diploma Programme Environmental Systems and Societies (SL) with this 2026 formula sheet. Covers all 8 topics, key calculations (NPP, ecological footprint, Simpson's index, Lincoln index), statistical methods… Always cross-check with your official syllabus and past papers for your exam session.
No. In the exam you must follow only what your exam board allows in the hall—usually the official formula booklet or data sheet where provided. This page is a revision and teaching aid, not a replacement for board-issued materials.
It is written for students preparing for assessments at Post-Secondary in Environmental Systems and Societies, including classroom revision, homework support, and independent study. Teachers and tutors can also share it as a quick reference.
Work through past paper questions, quote the correct formula before substituting values, and check units and notation every time. Pair this sheet with timed practice and mark schemes so you see how examiners expect working to be set out.
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Work through ESS topics, calculations and your Individual Investigation with an experienced IB DP ESS tutor. We focus on systems thinking, statistical analysis and integrating environmental + societal perspectives.
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This formula sheet aligns with IB Diploma Programme Environmental Systems and Societies (SL) syllabus content for 2026 examinations.
ESS is a transdisciplinary SL course — every answer should integrate environmental science with social, economic, political and cultural perspectives.