Population Density
How crowded a place is.
Formula
Population density = Total population / Land area (km²) Example: 50,000,000 / 500,000 = 100 people/km² Cambridge IGCSE Environmental Management 0680 / 0993
🌱 IGCSE Environmental Management Formula Sheet 2026
Population growth, density and Lorenz curves, BOD, energy efficiency, ecological footprint, sustainability indicators and exam keywords — your complete Cambridge IGCSE Environmental Management 2026 reference.
Population & Density Pollution Indices Energy Efficiency Sustainability
Our formula sheets are free to download — save this one as PDF for offline revision.
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.
All the Cambridge IGCSE Environmental Management Calculations & Theory in One Place
Cambridge IGCSE Environmental Management (0680 from 2026 first awards / 0993 final awards) blends quantitative analysis (rates, indices, efficiencies) with applied case-study theory (climate change, biodiversity loss, sustainability). This formula sheet brings every required equation, named indicator and key concept together so you can plan, calculate and evaluate every paper question.
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Population growth rates, density and demographic change
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Pollution: BOD, AQI, smog, eutrophication indicators
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Energy efficiency, EROI, renewable percentage
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Sustainability: ecological footprint, HDI, biocapacity
Population & Demographics
State units (people/km², %, per 1000) and time period in every answer.
Birth Rate / Death Rate
Per 1000 of population per year.
Birth rate
Birth rate = (Births in a year / Total population) × 1000 Death rate
Death rate = (Deaths in a year / Total population) × 1000 Natural Increase / Population Growth Rate
Natural increase rate (NIR)
NIR = (Birth rate − Death rate) / 10 (expressed as %) Example: BR 30, DR 8 → (30−8) / 10 = 2.2% growth Total growth rate
Growth rate (%) = NIR + Net migration rate (%) Doubling Time (Rule of 70)
Quick estimate of how long until a population doubles at constant growth.
Doubling time (years) ≈ 70 / Annual growth rate (%) Net Migration Rate
Net migration rate = (Immigrants − Emigrants) / Total population × 1000 Demographic Transition Model (DTM) Stages
Stage 1
High BR, high DR — pre-industrial, low growth Stage 2
High BR, falling DR — rapid growth (early industrialising) Stage 3
Falling BR, low DR — slowing growth Stage 4
Low BR, low DR — stable population Stage 5
BR below DR — declining population (e.g. Japan, Italy) Dependency Ratio
Higher ratio = more dependants per worker.
Dependency ratio = (Population <15 + Population ≥65) / Population 15–64 × 100 Population Pyramid Shapes
Wide base
High birth rate, young population (Stage 2 DTM) Narrow base
Low birth rate, ageing population (Stage 4/5) Bulges
Reflect cohorts (e.g. baby boom) Atmospheric & Air Pollution
Common Cambridge questions: identify the pollutant, give source, effect and management strategy.
Greenhouse Gas Concentrations
Measured in parts per million (ppm) or ppb.
Pre-industrial CO₂ ≈ 280 ppm · 2020s ≈ 420+ ppm % increase
(New − Old) / Old × 100 Major Air Pollutants
CO₂
Combustion of fossil fuels — greenhouse gas, climate change CH₄ (methane)
Livestock, paddy fields, landfill — 25× CO₂ warming potential N₂O
Fertilisers, combustion — greenhouse + ozone-depleting SO₂
Coal/oil burning — acid rain (H₂SO₃ / H₂SO₄) NOx
Vehicle exhausts, power stations — acid rain, smog CO
Incomplete combustion — toxic PM10 / PM2.5
Particulate matter — respiratory disease CFCs / HCFCs
Old refrigerants/aerosols — ozone depletion Air Quality Index (AQI)
Composite of pollutants — gives health-relevant air-quality band.
AQI uses worst-of: PM2.5, PM10, O₃, NO₂, SO₂, CO Bands (WHO indicative)
0–50 Good · 51–100 Moderate · 101–150 Unhealthy for sensitive · 151+ Unhealthy / Very unhealthy / Hazardous Acid Rain Chemistry
SO₂ + H₂O → H₂SO₃ (sulfurous acid) · further oxidised → H₂SO₄ (sulfuric acid) NO₂ + H₂O → HNO₃ (nitric acid) Effects: leaches Al³⁺ in soils, kills aquatic life below pH 5, corrodes limestone.
Ozone Depletion vs Global Warming
Ozone depletion
Loss of stratospheric O₃ — caused by CFCs/HCFCs — ↑ UV reaching surface Global warming
Rising surface T from greenhouse gases — different process; both involve atmospheric chemistry Smog Types
Photochemical (LA-type)
Sunlight + NOx + VOCs → ozone + secondary smog (warm, dry cities) Industrial (London-type)
SO₂ + smoke + temperature inversion (cold, damp) Water & Aquatic Pollution
Biochemical Oxygen Demand (BOD)
Oxygen consumed by microbes breaking down organic matter — high BOD = polluted water.
Formula
BOD (mg/L) = DO (initial) − DO (after 5 days at 20°C) Bands
<3 mg/L clean · 3–6 moderate · >6 polluted Dissolved Oxygen (DO)
Falls with: temperature ↑, organic pollution ↑, eutrophication Rises with: photosynthesis, turbulence, low temperature Eutrophication Sequence
Excess N & P (fertilisers, sewage) → algal bloom → blocks sunlight → submerged plants die → bacteria decompose → DO falls → fish & invertebrates die pH of Water Bodies
Healthy freshwater ≈ pH 6.5–8.5.
<6.5 = acidified (acid rain, mine drainage) >8.5 = alkaline (limestone, agricultural runoff) Water Treatment Sequence
Screening → Sedimentation/coagulation → Filtration (sand) → Disinfection (Cl₂, UV, O₃) → Distribution Sewage Treatment Stages
Primary
Physical settling — removes solids Secondary
Biological — bacteria break down organic matter (activated sludge / trickling filter) Tertiary
Removes N, P, pathogens — discharge into rivers Marine Pollution
Oil spills · Plastic / microplastics · Sewage · Industrial chemicals · Heavy metals · Thermal · Acoustic Energy & Resources
Always include units (J, kJ, kWh, %) and use the same base when calculating efficiencies.
Energy Conversions
1 kWh = 3.6 × 10⁶ J = 3.6 MJ 1 toe (tonne of oil equivalent) ≈ 41.87 GJ ≈ 11,630 kWh Energy Efficiency
% of input energy converted to useful output.
Formula
Efficiency (%) = (Useful energy out / Total energy in) × 100 Example: Power station — 600 MJ useful out / 1500 MJ in = 40% EROI (Energy Return On Investment)
Higher EROI = more useful per unit invested. Hydro often >100; tar sands ~3–5.
EROI = Energy delivered / Energy used to deliver it Capacity Factor (renewables)
Wind ~25–45% · Solar PV ~10–25% · Hydro ~30–60% (varies widely).
Capacity factor (%) = (Actual output over period / Maximum possible output) × 100 Renewable Energy %
Renewable share (%) = (Renewable energy / Total energy) × 100 Carbon Intensity of Electricity
kg CO₂ / kWh — coal ~0.9 · gas ~0.4 · nuclear ~0.01 · solar/wind ~0.04 Resource Reserve : Production Ratio (R/P)
Estimate of how long current reserves last at current rate.
R/P (years) = Proven reserves / Annual production Energy Sources Summary
Non-renewable
Coal · Oil · Natural gas · Nuclear (uranium) Renewable
Solar · Wind · Hydro · Geothermal · Biomass · Tidal · Wave Ecosystems, Biodiversity & Land Use
Ecological Footprint
Land area needed to sustain a population's resource use and waste.
Measured in global hectares (gha) per person Compare to biocapacity (gha/person available) — overshoot if footprint > biocapacity Biocapacity
Biocapacity = Land productivity × Productive area (gha) Biodiversity Indices
Species richness
Number of different species in an area Simpson's Index (D)
D = 1 − Σ(n/N)² where n = individuals of each species, N = total individuals — closer to 1 = more diverse Shannon-Wiener (H)
H = −Σ(p × ln p) — higher H = more diverse Population Sampling — Lincoln Index
Estimate animal population by mark-release-recapture.
Formula
Population (N) = (M × n) / m M = first sample marked · n = second sample size · m = marked individuals re-caught Quadrat Sampling
Density
Density = Total individuals / (Number of quadrats × Quadrat area) Frequency
Frequency (%) = (Quadrats with species / Total quadrats) × 100 % cover
Estimated within each quadrat — average across all quadrats Ecological Productivity
GPP
Gross Primary Productivity — total energy fixed by plants NPP
NPP = GPP − Respiration losses (the energy available for next trophic level) Energy transfer
~10% energy passed to next trophic level — explains short food chains Deforestation Rate
Annual deforestation rate (%) = (Forest loss in year / Original forest area) × 100 Soil Erosion Rate
Tonnes per hectare per year — sustainable rate < natural soil formation rate Climate & Weather
Greenhouse Effect (Natural & Enhanced)
Sun's shortwave radiation in → absorbed by Earth → re-emitted as longwave (IR) → trapped by GHGs (CO₂, CH₄, N₂O, H₂O vapour) → warms atmosphere Albedo
% of incoming radiation reflected.
Snow/ice ~80–90% · Desert ~30% · Forest ~10–15% · Ocean ~6–10% Ice-albedo feedback: melting ice → lower albedo → more warming → more melting.
Temperature Anomaly
Used in climate-change graphs (e.g. 1.2°C above pre-industrial).
Anomaly = Observed T − Long-term mean T Wind & Pressure
Wind
Air moves from high to low pressure — speed depends on pressure gradient Coriolis effect
Deflection of moving air — right in NH, left in SH Climate Feedback Loops
Positive (amplifies)
Ice-albedo, permafrost methane release, water vapour Negative (stabilises)
Increased cloud cover (some scenarios), CO₂ uptake by plants/oceans Sustainable Development & Economics
Three Pillars of Sustainability
Environmental · Economic · Social — must all balance for true sustainability Human Development Index (HDI)
UN composite measure (0–1).
HDI combines: Life expectancy + Education (mean & expected schooling years) + GNI per capita (PPP) GDP / GNI per Capita
GDP per capita
Total GDP / Population PPP-adjusted
Compares living standards across countries (purchasing power parity) Carbon Footprint per Capita
Global average ~4.5 t · USA ~15 · India ~2 · Low-income countries <1.
CF per capita (t CO₂e/yr) = Total emissions / Population Recycling & Waste Hierarchy
Reduce → Reuse → Recycle → Recover (energy from waste) → Dispose (landfill last resort) Recycling rate
Recycled mass / Total waste mass × 100 Water Footprint
Total fresh water used to produce goods/services for an individual or country (m³/person/year) UN Sustainable Development Goals (SDGs)
17 goals (2015–2030): poverty, hunger, health, education, gender, water, energy, work, infrastructure, inequality, cities, consumption, climate, marine, terrestrial, peace/justice, partnerships Statistical & Graphical Tools
Mean / Median / Mode / Range
Mean
Σx / n Median
Middle value when ordered Mode
Most common value Range
Max − Min Percentage Change
% change = ((New − Old) / Old) × 100 Rate Calculations
Rate
Rate = Change in quantity / Time taken Examples: erosion (mm/yr), sea-level rise (mm/yr), deforestation (ha/yr) Choropleth & Isoline Maps
Choropleth
Shaded by category (e.g. CO₂ emissions per country) — categorical comparison Isoline
Lines of equal value (contours, isobars) — continuous data Scatter Diagrams & Correlation
Positive
Both variables ↑ together (e.g. CO₂ vs temperature) Negative
One ↑ as other ↓ (e.g. tree cover vs erosion) No correlation
No clear pattern Correlation ≠ causation. Always state the strength (strong/weak) and direction.
Cambridge Exam Technique & Keywords
Match your structure to the command word — Cambridge mark schemes reward precise terminology.
Command Word Quick Guide
State / Name
One-word or short factual answer Describe
Give details — use data from a graph/table where present Explain
Give reasons — use 'because', 'this leads to', 'as a result' Compare
Similarities AND differences — use comparative phrases ('higher than', 'whereas') Evaluate
Strengths AND weaknesses → reasoned overall judgement Suggest
Apply knowledge to a new context with reasoning Discuss
Pros + cons + concluding view Standard 6-Mark Question Frame
Cambridge usually wants 3 distinct points × 2 marks each (point + development/example/data) Use Data, Not Vague Statements
Always quote figures from a graph/table — 'CO₂ rose from 320 ppm in 1960 to 420 ppm in 2024 — a 31% increase' Specific data > vague 'a lot' or 'many'.
Two-Sided Sustainability Answers
Almost every long evaluation question wants BOTH benefits and drawbacks across all 3 sustainability pillars Case Study Bank
Prepare 1–2 named case studies for each topic: e.g. Aral Sea (water), Amazon (deforestation), Maldives (sea-level), Costa Rica (eco-tourism), Bangladesh (climate vulnerability) How to Use This Formula Sheet
Boost your Cambridge exam confidence with these proven study strategies from our tutoring experts.
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Master the Standard Calculations
Population density, NIR, BOD, efficiency, % change and Lincoln Index appear every year. Practise until each is automatic — show units and working.
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Build a Case Study Bank
Prepare 1–2 named global case studies per topic (e.g. Amazon for deforestation, Maldives for sea-level rise). Examiners reward specific examples over vague claims.
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Always Use Data from the Graph
When a question shows a graph or table, quote at least one figure with units in your answer. Vague 'a lot' or 'big increase' caps your mark.
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Two-Sided Evaluation
For 'evaluate' or 'discuss' questions, give benefits AND drawbacks across all 3 pillars (environmental, economic, social) before reaching a justified conclusion.
Formula Sheet FAQ
Quick answers about this free PDF and how to use it for exam revision and active recall.
Is the IGCSE Environmental Management Formula Sheet 2026 free to download as a PDF?
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.
What Environmental Management topics and equations does this formula sheet cover?
This page groups key Environmental Management formulas in one place for revision. Master Cambridge IGCSE Environmental Management (0680/0993) with this 2026 formula sheet. Covers population, growth and density calculations, BOD, energy efficiency, ecological footprint, sustainability indicators and… Always cross-check with your official syllabus and past papers for your exam session.
Can I use this instead of the official exam formula booklet in the exam?
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.
Who is this formula sheet for (Secondary)?
It is written for students preparing for assessments at Secondary in Environmental Management, including classroom revision, homework support, and independent study. Teachers and tutors can also share it as a quick reference.
How should I revise with this formula sheet?
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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This formula sheet aligns with Cambridge Assessment International Education IGCSE Environmental Management (0680 from 2026 first awards / 0993 final awards) syllabus content for 2026 examinations.
Always show working in calculations and state units (people/km², mg/L, %, t CO₂e/yr) — and quote graph/table data verbatim in extended answers.