Biology Calculator Hub
Interactive tools for genetics, ecology, microbiology, physiology, and biostatistics – built for students, teachers, and researchers.
Quick Biology Explorer
Use this mini “biology workbench” to explore exponential growth/decay, doubling time, and half‑life – concepts that appear in cell culture, population biology, pharmacokinetics, and radioactive tracers.
e.g., starting cell count, initial concentration, or population size.
Leave blank if you are solving for N(t).
Leave blank if you are solving for time.
Positive k. Leave blank if you are solving for k.
Results
Solved value
Doubling time / Half‑life
Computed from k using \( t_{1/2} = \frac{\ln 2}{k} \). For growth, this is doubling time; for decay, it is half‑life.
Conceptual model
Exponential growth/decay is described by:
N(t) = N₀ · e±k·t
- Growth: N(t) = N₀ · e+k·t
- Decay: N(t) = N₀ · e−k·t
- Doubling time / half‑life: t1/2 = ln(2) / k
Featured biology calculators on CalcDomain
Browse specialized tools for molecular biology, ecology, and biostatistics. Each calculator includes formulas, worked examples, and unit‑aware inputs.
DNA to Protein Translator
Convert DNA or mRNA sequences into amino acid chains using the standard genetic code.
Molecular biologyDNA Concentration
Estimate DNA concentration from absorbance (A260) or mass/volume for qPCR and cloning.
Lab prepHemocytometer Cell Counting
Convert counted cells in grid squares into cells/mL and total cell numbers.
Cell cultureMolecular Weight
Compute molecular weight from chemical formulas for buffer and reagent preparation.
ChemistryMolarity
Convert between mass, volume, and molar concentration for solutions.
SolutionsSolution Dilution
Use C₁V₁ = C₂V₂ to plan serial dilutions and working solutions.
DilutionsSerial Dilution
Design multi‑step dilutions for microbiology, ELISA, and qPCR.
MicrobiologyqPCR ΔΔCt Analysis
Compute relative gene expression using the 2−ΔΔCt method.
Gene expressionPunnett Square
Visualize Mendelian inheritance for mono‑ and dihybrid crosses.
GeneticsAllele Frequency
Calculate allele and genotype frequencies in populations.
Population geneticsHardy–Weinberg Equilibrium
Model genotype frequencies under random mating and no selection.
Population geneticsLotka–Volterra Predator–Prey
Simulate coupled predator–prey dynamics and phase plots.
EcologyShannon Diversity Index
Quantify species diversity in ecological communities.
BiodiversitySimpson’s Diversity Index
Measure dominance and evenness in species assemblages.
BiodiversityMichaelis–Menten Kinetics
Explore enzyme kinetics and saturation curves.
EnzymologyELISA Data Analysis
Fit standard curves and interpolate sample concentrations.
ImmunoassaysMark–Recapture (Lincoln–Petersen)
Estimate population size from capture–recapture data.
Field ecologyBacterial Growth Curve
Model lag, exponential, and stationary phases in cultures.
MicrobiologyCell Doubling Time
Estimate doubling time from cell counts at two time points.
Cell biologyWhat is biology?
Biology is the study of life. It spans scales from molecules and cells to organisms, populations, ecosystems, and the biosphere. Modern biology is highly quantitative: you routinely estimate growth rates, concentrations, probabilities, and uncertainties. This page focuses on the calculations that support biological thinking and experimentation.
Core quantitative ideas in biology
- Exponential change – cell cultures, viral load, drug clearance, and radioactive tracers often follow exponential growth or decay.
- Probabilities – inheritance patterns, mutation events, and sampling in ecology are naturally probabilistic.
- Concentrations and dilutions – nearly every wet‑lab protocol relies on molarity, mass/volume, and serial dilutions.
- Rates and fluxes – enzyme kinetics, metabolic flux, and population dynamics are expressed as rates per time or per biomass.
Exponential growth and decay in biology
Many biological processes can be approximated by the exponential model implemented in the explorer above:
General form
N(t) = N₀ · er·t
- Growth: r > 0 (e.g., bacteria in log phase)
- Decay: r < 0 (e.g., drug concentration after a bolus dose)
- Doubling time: td = ln(2) / r
- Half‑life: t1/2 = ln(2) / |r|
In practice, you often estimate r from two measurements:
r = (1 / Δt) · ln(N₂ / N₁)
where N₁ and N₂ are the amounts at times t₁ and t₂, and Δt = t₂ − t₁.
Example: estimating bacterial doubling time
Suppose an E. coli culture grows from 1×10⁶ to 8×10⁶ cells/mL in 6 hours.
- Compute r: r = (1/6) · ln(8×10⁶ / 1×10⁶) = (1/6) · ln(8) ≈ 0.3466 h⁻¹.
- Compute doubling time: td = ln(2) / r ≈ 0.6931 / 0.3466 ≈ 2.0 hours.
The interactive explorer reproduces this calculation and lets you change N₀, N(t), and t to match your own data.
How these biology calculators can help you
- Students – check homework, visualize models, and connect equations to real biological scenarios.
- Instructors – generate clean examples and plots for lectures, labs, and exams.
- Researchers – perform quick back‑of‑the‑envelope checks when designing experiments or interpreting data.
Limitations and good practice
- Always check that model assumptions (e.g., constant growth rate, well‑mixed population, no resource limitation) are reasonable.
- Use units consistently and document them in lab notebooks and reports.
- For critical decisions (clinical, regulatory, or high‑stakes research), validate results with independent methods or domain experts.
Biology calculators – FAQ
Do these tools replace full biology textbooks or lab manuals?
No. They complement textbooks and protocols by handling the arithmetic and visualization, so you can focus on concepts and experimental design. For rigorous study, use them alongside trusted references such as OpenStax Biology, Khan Academy, or primary literature.
Can I change units (hours, minutes, days) in the growth/decay explorer?
Yes. Choose the time unit for t and k from the dropdowns. The calculator internally converts units so that the rate constant and time are consistent before computing N(t), t, or k.
How accurate are the default values?
Defaults are illustrative and chosen to produce realistic‑looking numbers (for example, typical bacterial doubling times of 20–60 minutes, or multi‑hour drug half‑lives). Always replace them with values measured or reported for your specific organism, tissue, or compound.
Can I export results or screenshots?
You can copy numerical outputs directly into spreadsheets or lab notebooks. For plots and interactive tools on other biology pages (e.g., Lotka–Volterra, Michaelis–Menten), use your browser’s screenshot or print‑to‑PDF features to capture figures for reports and slides.