Biology Calculators

Cross two parent genotypes for a single gene and get the offspring genotype ratio, phenotype ratio and the odds of dominant versus recessive traits.

Work out allele and genotype frequencies under Hardy-Weinberg equilibrium from a dominant allele frequency p or from the frequency of the recessive phenotype q².

Count homozygous and heterozygous individuals to get the dominant and recessive allele frequencies and the genotype frequencies of a population.

Project a population growing exponentially from its starting size, growth rate and number of periods, with the total increase and doubling time.

Model population growth that slows as it approaches a carrying capacity, using the logistic equation to find the size at any time and how close it is to the ceiling.

Estimate how many bacteria are present after a period of exponential division from the starting count, doubling time and elapsed time.

Calculate the surface-area-to-volume ratio of a sphere or cube and see why small cells exchange materials with their surroundings far more efficiently.

Find the total magnification of a compound microscope from the eyepiece and objective, plus the field-of-view diameter when you switch objectives.

Estimate how many DNA copies a PCR run produces from the starting template, number of cycles and amplification efficiency.

Molecular weight of DNA or RNA from its length or from the exact sequence — dsDNA, ssDNA or RNA, 5′ end chemistry, linear or circular — with mass ↔ pmol ↔ copy-number conversions, molarity from ng/µL, base composition and the A260 extinction coefficient of an oligo.

Find the reaction velocity of an enzyme from Vmax, the Michaelis constant Km and the substrate concentration, plus how close it runs to its maximum rate.

Work out the dilution factor from your sample and diluent volumes, and the final concentration after diluting a stock solution.

Estimate a wild population from mark-recapture data: the Lincoln-Petersen index and the less biased Chapman estimate with standard error and a 90, 95 or 99% confidence interval, or Schnabel and Schumacher-Eschmeyer estimates from several sampling occasions.

Calculate the respiratory quotient from carbon dioxide produced and oxygen consumed, and read off which fuel the body is mainly burning.

Estimate the due date for humans, dogs, cats, cows or horses from the breeding or last-period date and the species gestation length.

Cross two parent genotypes for a single gene and get the genotype ratio, phenotype ratio, trait probabilities and the expected number of each offspring type in a chosen brood size.

Estimate allele frequencies p and q and the expected genotype counts under Hardy-Weinberg equilibrium from the number of recessive (homozygous) individuals in a population.

Calculate the doubling time of a growing cell culture from an initial count, a final count and the elapsed time, plus the number of doublings and the specific growth rate.

Project a bacterial population forward from a starting count using the generation (doubling) time, and get the final count, the number of generations and the growth-rate constant.

Convert a spectrophotometer A260 reading into nucleic-acid concentration using the Beer-Lambert factor, with total yield and the A260/A280 purity ratio.

Estimate the molar mass of a DNA fragment from its length in base pairs, then convert a sample mass into moles, picomoles and the number of copies.

Work out how much stock and how much diluent to mix for a target concentration using C1V1 = C2V2, with the dilution factor expressed as a 1:X ratio.

Compute the concentration at each tube of a serial dilution series from a starting concentration, a fixed fold factor per step and the number of steps.

Find the growth rate of a population from an initial size, a final size and the time between them — both the continuous rate r and the percent change.

Calculate enzyme activity in units (µmol product per minute) and specific activity per milligram of protein from the product formed, reaction time and enzyme amount.

Compute allele frequencies p and q from observed genotype counts, and compare the observed genotype frequencies against the Hardy-Weinberg expectation.

Convert a hemocytometer count into cells per millilitre and the total number of cells in a culture, using the counted cells, squares counted and dilution factor.

Cross two parents across two independent genes and get the phenotype ratio, the probability of each of the four trait combinations and the expected offspring counts for a chosen brood size.

Cross an organism of unknown genotype against a fully recessive tester and get the expected phenotype ratio, number of phenotype classes and offspring counts that reveal how many genes are heterozygous.

Enter both parents' ABO blood-type genotypes and get the probability that a child is type A, B, AB or O, with the exact allele combinations behind each outcome.

Paste a DNA sequence and get its GC content percentage, AT content, base counts and a Wallace-rule melting temperature estimate for short primers and oligonucleotides.

Transcribe a DNA template strand into its mRNA, or convert a coding length in base pairs into mRNA nucleotides, codons and the resulting protein length.

Convert an mRNA length in nucleotides into the number of codons and the length of the encoded protein, or work backwards from a known protein length to the coding nucleotides needed.

Turn a mass of solute, its molecular weight and a solution volume into molarity for cell-culture media and buffers — with the result in mol/L, mM and µM plus total moles.

Model a cell as a sphere or cube and get its surface area, volume and surface-area-to-volume ratio — the number that explains why small cells exchange materials faster than large ones.

Enter the volume of CO₂ produced and O₂ consumed and get the respiratory quotient plus the fuel it points to — carbohydrate, fat or mixed substrate oxidation.

Estimate an animal's basal metabolic rate from its body mass using Kleiber's law (rate ∝ mass^0.75) — in kilocalories per day, kilojoules per day and watts.

From the amount of CO₂ fixed, estimate the photons and light energy photosynthesis needs, along with the glucose synthesised and oxygen released, using the ~8-photon quantum requirement.

Multiply eyepiece, objective and any intermediate lens power to get total microscope magnification, and use the field number to find the field-of-view diameter at that setting.

Work out population density from a head count and an area in any common unit, and see the equivalent density per square kilometre and per square mile.

Use the logistic growth model to find how fast a population is growing at its current size, its per-capita growth rate and the maximum growth rate at half the carrying capacity.

Estimate a total wildlife population from a mark-recapture study using both the Lincoln-Petersen index and the less-biased Chapman estimator.

Compute Simpson's dominance index, Simpson's index of diversity (1 − D) and the reciprocal Simpson index (1/D) from a list of species abundances.

Calculate the Shannon-Wiener diversity index (H), Pielou's evenness and the effective number of species from a list of species abundances.

Find the predator-to-prey ratio, the number of prey supporting each predator and the predator count per 100 prey from two population counts.

Convert a percentage growth rate into a doubling time using the exact continuous and discrete formulas, plus the quick rule-of-70 approximation.

Find the generation (doubling) time of a growing population from its starting and final size over a measured interval, plus the number of generations and the growth rate constant.

Estimate your annual carbon footprint in tonnes of CO₂ and how many Earths your lifestyle would need, from driving, home electricity, flights and diet.

Compute a body mass index for an animal from its weight and body length, plus the weight-per-length and surface-area-to-volume scaling that shape its physiology.

Estimate an animal's basal metabolic rate from its body mass using Kleiber's ¾-power allometric law, and see the mass-specific rate that explains why small animals burn energy faster.

Predict a mammal's or bird's resting heart rate from body mass with published allometric equations (a × M^b), plus beat interval, beats per day and year, breathing rate, heart mass, ECG intervals and the near-constant billion-beat lifetime.

Estimate the melting temperature of a short PCR primer from its base composition using the Wallace (2+4) rule.

Set the annealing temperature for a PCR reaction from your two primer melting temperatures.

Work out how many fragments a restriction enzyme produces and their average size, plus how often a site is expected to occur.

Estimate the size of an unknown DNA band from its migration distance using a two-point log(size) standard curve.

Estimate a protein’s molecular weight in daltons and kilodaltons from its number of amino acid residues.

Estimate a protein’s isoelectric point from the counts of its ionizable amino acids using Henderson–Hasselbalch.

Convert an OD600 absorbance reading into cells per millilitre and total cells using a calibration factor.

Calculate transformation efficiency in colony-forming units per microgram of DNA from your plate counts.

Find how much viral stock to add for a target MOI, and the Poisson fraction of cells that get infected.

Back-calculate colony-forming units per millilitre from a plate count, the volume plated and the dilution factor.

Compute the doubling time and specific growth rate of a culture from two OD600 readings and the time between them.

Solve for Michaelis constant Km and maximum velocity Vmax from two substrate–velocity data points by the double-reciprocal method.

Convert an absorbance at 280 nm into protein concentration (mg/mL and µM) with ε (0.1%), E1% or molar ε + molecular weight, or BSA, IgG and lysozyme presets — with dilution, path length and baseline corrections, A260/A280 purity check and Warburg–Christian estimate.

Compute DNA or RNA concentration from A260 plus the 260/280 and 260/230 purity ratios — with A320 background correction, path length, dilution, yield, molarity and copies per µL, a dilution recipe and a ready-or-clean-up check for PCR, qPCR, sequencing, cloning and transfection.

Work out how many nanograms of insert to add for a chosen insert:vector molar ratio from the fragment sizes and vector mass.

Percent cell viability from trypan blue live/dead counts, automated-counter concentrations or an MTT/MTS/resazurin plate assay — with viable and dead cells per mL, total viable cells, a 95% confidence range, seeding volume and replicate statistics.

Turn hemocytometer (Neubauer) counts into cells per mL and total cells — any square size, dilution factor or trypan blue mix volumes, live/dead viability, counting error and a seeding plan with the volume to pipette.

How many cells to seed per well, dish or flask — by cells/cm², cells per vessel or % confluence — with the stock and medium volumes for a master mix or per-well pipetting, viability correction, a scale-up table for every plate format and a projected confluence curve.

Plan a passage: from current confluence, doubling time and when you next need the cells, find the split ratio, cells per flask and expected confluence at pickup.

Volumes of antibody stock and buffer for a 1:X dilution, a working concentration (ng/mL to mg/mL) or an amount per test, for any number of samples with overage. Adds a secondary antibody, an intermediate dilution when the volume is too small to pipette, a titration series and the cost per run.

Recombination frequency from parental and recombinant offspring counts, converted to map units (centimorgans) with the Haldane correction for double crossovers.

Test observed offspring counts against an expected Mendelian ratio (3:1, 1:2:1, 9:3:3:1, 1:1 or custom) — χ², degrees of freedom and p-value.

Broad-sense and narrow-sense heritability from variance components, or realised heritability from a selection experiment via the breeder’s equation.

Effective population size (Ne) from unequal sex ratios and from fluctuating census sizes over generations, with the Ne/N ratio and loss of heterozygosity per generation.

Estimate population size and density from quadrat counts — mean per quadrat, density per m², total for the study area, and a 95% confidence range.

Calculate net primary productivity (NPP) from GPP and autotrophic respiration, GPP and carbon-use efficiency, biomass change with litterfall, or light and dark bottle oxygen readings. Gives g C/m²/yr, dry matter, CO₂ fixed, O₂ released, t C/ha, area totals, NEP and the closest ecosystem type.

Compute Q10 from reaction or metabolic rates at two temperatures, or predict a rate at a new temperature from a known Q10.

Build a BSA standard curve from your absorbance readings, get the linear fit and R², and convert sample absorbances into protein concentrations with dilution factors.

Predict a protein’s ε at 280 nm from a pasted amino-acid sequence or from its tryptophan, tyrosine and cystine counts (Pace / ProtParam or Gill & von Hippel), with molecular weight, Abs 0.1%, oxidised vs reduced values and the concentration from an A280 reading.

Copies and nanograms of PCR product after n cycles from template copies or template mass, with amplification efficiency, the plateau set by product, primer and dNTP limits, the cycle a gel band appears, cycles needed for a target amount and a cycle-by-cycle table.

Convert nanograms of DNA (plasmid, genomic or amplicon) into molecule copies from the fragment length — and back from copies to mass — for qPCR standards and dilution series.

Resting membrane potential from K⁺, Na⁺ and Cl⁻ concentrations and relative permeabilities using the GHK voltage equation, with each ion’s Nernst potential for comparison.

Water potential of a solution or cell from solute potential (van’t Hoff: −iCRT) and pressure potential — direction of water movement between two compartments and the equilibrium condition.

Fit Km and Vmax from substrate concentrations and reaction velocities via the double-reciprocal plot — slope, intercepts, R², kcat and catalytic efficiency.

Enzyme units from an absorbance rate (ΔA/min, ε, path length, volumes) and specific activity in U/mg — with fold purification and yield across purification steps.

Estimate true species richness from abundance counts or from singletons and doubletons: Chao1 (classic and bias-corrected, with the (n−1)/n small-sample factor), variance, log-linear 95% confidence interval, ACE, unseen species and sample coverage (Good and Chao–Jost).

Basal metabolic rate of a mammal, marsupial, bird or reptile from body mass with Kleiber’s ¾-power law: watts, kcal and kJ per day, oxygen use, mass-specific rate, daily energy at a field multiple, comparison with another animal, and a table from mouse to elephant.

Reverse complement, complement or reverse of DNA or RNA — paste one sequence or several FASTA records — with IUPAC codes, DNA/RNA output, case kept, grouping in blocks or codons, plus length, base counts, GC content, basic and salt-adjusted Tm, molecular weight and a palindrome check.

Percent identity and similarity of two DNA, RNA or protein sequences: paste an existing alignment or let the tool align them (Needleman–Wunsch, BLOSUM62), with identity over the alignment, ungapped columns, the shorter, mean or longer sequence, gaps, alignment score, p-distance with Jukes–Cantor, Kimura or Poisson correction, transitions and transversions, and the alignment itself.

Convert a NanoDrop or spectrophotometer A260 reading into ng/µL of dsDNA, ssDNA, RNA or oligonucleotide, judge purity from the A260/A280 and A260/A230 ratios, and work out the volume needed for a given mass of nucleic acid.

Pick the agarose percentage for the DNA fragment sizes you need to resolve, or set your own, then get the grams of agarose, buffer stock and water (1× TAE or 0.5× TBE from 50×, 10× or 5× stocks), the DNA stain volume, the running buffer for the tank and the voltage, for any tray size and number of gels.

Pick the acrylamide percentage that resolves your protein (or two proteins), then get resolving and stacking gel recipes from a 30% or 40% stock: Tris, SDS, APS, TEMED and water. Sambrook or Bio-Rad conventions, scaled to your gel count and cassette size.

Scale a lipid transfection master mix for any plate format — DNA µg per well, reagent µL at your chosen reagent:DNA ratio, serum-free dilution medium volumes, plasmid stock volume from its concentration — with a 10% overage and cell seeding guidance.

Use the species–area relationship S = c·Aᶻ to predict how many species a habitat of a given area holds, fit c and z from two surveys, and estimate the species lost when habitat shrinks (the extinction debt from area loss) — with typical z values for islands, mainland plots and habitat fragments.

Calculate basal area per hectare or acre from a list of tree diameters (DBH) on one or more fixed plots, or from a prism / angle-gauge count with any basal area factor (metric or BAF 10), with trees per hectare and acre, quadratic mean diameter, Reineke stand density index, relative density, stocking class, a diameter-class table and a thinning target from below, from above or by average tree.

Calculate leaf area index from canopy light transmission (Beer–Lambert, with a fixed extinction coefficient or one from the sun angle and leaf angle distribution, plus a clumping correction), from harvested leaf area or leaf dry mass × specific leaf area over ground area, or from leaf area per plant × plant density. Shows light interception, the LAI for 95% interception, an interception curve and typical LAI values for crops and forests.

Trace energy up a food chain with the 10% rule (or your own transfer efficiency per level) — energy or biomass available at each trophic level, how much producer biomass supports a top consumer, the land or ocean area implied, why food chains rarely exceed 4–5 links, and the plant-vs-meat diet comparison.

Solve the Lotka–Volterra predator–prey model — equilibrium prey and predator numbers, the oscillation period, the current growth rates of both populations from their sizes, and a simulated table of the cycle — from prey growth rate, predation rate, conversion efficiency and predator mortality.

Calculate the inbreeding coefficient F with Wright’s path formula: pick the parents’ relationship, list each common ancestor with its generations to the sire and dam, or paste a whole pedigree. Also gives the recessive-disease risk, the loss of heterozygosity and how F builds up in a small population.

Predict genetic gain with the breeder's equation R = h²S — the response per generation from heritability and the selection differential, or from the proportion selected via selection intensity and the trait's standard deviation — plus generations to reach a target, gain per year with the generation interval, and the realised heritability from observed gain.

Convert a soil test into carbon stock — soil organic matter or organic carbon percentage, bulk density, sampling depth and stone content to tonnes of carbon and CO₂-equivalent per hectare, the change between two samplings as a sequestration rate, and what a 0.4% per year (4 per 1000) target means for your field.

Calculate the mitotic index from cell counts in prophase, metaphase, anaphase, telophase and interphase, and estimate how long each phase of the cell cycle lasts from the total cycle time.

Use Fick's first law, rate = D × A × ΔC ÷ Δx, to find the diffusion rate and flux of oxygen, CO₂ or glucose across a membrane from surface area, concentration difference and thickness.

Build a PCR master mix for any number of reactions: µL of buffer, dNTPs, primers, MgCl₂, polymerase and water per reaction and for the whole mix, with extra volume for pipetting loss.

Calculate relative gene expression from qPCR Ct values with the Livak 2^−ΔΔCt method: ΔCt, ΔΔCt, fold change and log2 fold change, with an optional amplification efficiency.

Calculate qPCR primer amplification efficiency from a dilution-series standard curve or a slope: E = 10^(−1/slope) − 1, with slope, R², intercept and the 90–110% acceptance check.

Calculate virus titre as TCID50/mL from an endpoint dilution assay using the Spearman–Kärber and Reed–Muench methods, with log titre, 50% endpoint and an estimated PFU/mL.

Find how many µL of water or TE buffer to add to a dried oligo or primer (nmol on the spec sheet) for a 100 µM stock, its ng/µL, total µg, and how to make a 10 µM working dilution.

Calculate the degree of labeling (DOL, F/P ratio) of a fluorescent-dye–labeled antibody or protein from A280 and dye absorbance, with the A280 correction factor and protein concentration.