Environmental Science

Sustainability, energy, ecology, and earth-science formulae.

Environmental Science formulas bring together the key equations used to understand sustainability, energy systems, ecosystems, and Earth processes, from carbon footprint and pH to wind turbine power, solar output, and population growth. This category helps students, exam candidates, and professionals turn real-world environmental problems into measurable calculations, making it easier to assess impact, compare solutions, and make smarter decisions about resources and the planet.

Carbon Footprint

CO_2 = E \times f

Emissions from energy use and an emission factor.

Wind Turbine Power

P = \frac{1}{2}\rho A v^3 C_p

Power extracted from wind by a turbine.

Betz Limit

C_{p,max} = 0.593

Maximum fraction of wind energy a turbine can capture.

Solar Panel Output

P = A \times r \times H \times PR

Energy output of a photovoltaic array.

Radioactive Decay

N = N_0\left(\frac{1}{2}\right)^{t/t_{1/2}}

Amount remaining after a number of half-lives.

pH

pH = -\log_{10}[H^+]

Acidity from hydrogen ion concentration.

Energy Consumption

E = P \times t

Electrical energy used over time.

Exponential Population Growth

N = N_0 e^{rt}

Growth of a population at a constant rate.

Logistic Growth

\frac{dN}{dt} = rN\left(1 - \frac{N}{K}\right)

Population growth that slows as it nears carrying capacity.

Water Use Intensity

WUI = \frac{V_{water}}{Output}

Water consumed per unit of product or service.

Albedo

\alpha = \frac{\text{reflected}}{\text{incident}}

Fraction of solar radiation reflected by a surface.

Energy Payback Ratio

EPR = \frac{E_{generated}}{E_{invested}}

Energy produced over a lifetime divided by energy to build it.

Sound Level

L = 10\log_{10}\frac{I}{I_0}

Sound intensity level in decibels.

Richter Magnitude Energy

\log_{10}E = 4.8 + 1.5M

Approximate energy released by an earthquake.

Dilution Equation

C_1 V_1 = C_2 V_2

Relates concentration and volume before and after dilution.