Scientific References
Every BioSyn calculator cites where its formula and constants come from. This page collects those references in one place, grouped by tool and graded by tier. External links open in a new tab and carry rel="nofollow". We grade sources the same way on every page — see the about page for the A/B/C definitions and the methodology page for how we apply them.
How to read the tiers
- Tier 1 — Authoritative. NIST, NIH, NCBI, PubMed-indexed peer-reviewed papers. The basis for physical constants and reference methods.
- Tier 2 — Established technical. NEB, Thermo Fisher, Promega, IDT, Bio-Rad, Sigma/Merck. The basis for protocol conventions and conversion factors.
- Tier 3 — Supporting. Reputable educational resources. Used to cross-check or explain, never as a sole source for a constant.
References by calculator
Molarity Calculator
Method: M = n / V = m / (MW × V) · version 1.0 · reviewed 2026-09
- Promega Biomath — Molarity Calculator · Tier 2
- NEB NEBioCalculator · Tier 2
- NIST Chemistry WebBook · Tier 1
Dilution Calculator
Method: DF = C₁ / C₂ = V_final / V_stock; C₂ = C₁ / DF; V_stock = V_final / DF · version 1.0 · reviewed 2026-09
- Promega Biomath — Dilution Calculator · Tier 2
- NEB NEBioCalculator · Tier 2
- NIST Chemistry WebBook · Tier 1
C1V1 Calculator
Method: C₁V₁ = C₂V₂ · version 1.0 · reviewed 2026-09
- Promega Biomath — Dilution Calculator · Tier 2
- NEB NEBioCalculator · Tier 2
- NIST Chemistry WebBook · Tier 1
Molar Mass Calculator
Method: M = Σᵢ (nᵢ × Aᵢ) · version 1.0 · reviewed 2026-09
- NIST Chemistry WebBook · Tier 1
- CIAAW — Standard Atomic Weights · Tier 1
Stock Solution Calculator
Method: molar: m = (M × V × MW) / purity; % w/v: m = (% × V_mL / 100) / purity · version 1.0 · reviewed 2026-09
- Promega Biomath — Molarity Calculator · Tier 2
- NEB NEBioCalculator · Tier 2
- NIST Chemistry WebBook · Tier 1
Serial Dilution Calculator
Method: C_n = C₀ / DF^n; overall DF = DF^n; V_transfer = V_tube / DF; n = ceil( log(C₀/C_target) / log(DF) ) · version 1.0 · reviewed 2026-09
- Promega Biomath — Dilution Calculator · Tier 2
- NEB NEBioCalculator · Tier 2
- NIST Chemistry WebBook · Tier 1
Percent Solution Calculator
Method: w/v: mass_g = %/100 × V_mL; v/v: V_solute_mL = %/100 × V_mL; w/w: mass_g = %/100 × batch_g; M(w/v) = (mass_g / V_L) / MW · version 1.0 · reviewed 2026-09
- Promega Biomath — Dilution Calculator · Tier 2
- NEB NEBioCalculator · Tier 2
- NIST Chemistry WebBook · Tier 1
PPM Calculator
Method: ppm = mass_mg / V_L; % = ppm / 10,000; mass_mg = ppm × V_L; M = (ppm/1000) / MW · version 1.0 · reviewed 2026-09
- Promega Biomath — Dilution Calculator · Tier 2
- NEB NEBioCalculator · Tier 2
- NIST Chemistry WebBook · Tier 1
Primer Tm Calculator
Method: Tm = (ΔH × 1000) / (ΔS + R·ln(Ct/4)) − 273.15; ΔS = ΔS_NN+init + 0.368·(N−1)·ln[Na⁺] · version 1.0 · reviewed 2026-09
- SantaLucia J. (1998) PNAS 95:1460–1465 — unified DNA nearest-neighbour thermodynamics · Tier 1
- Primer3 — melting temperature calculation (SantaLucia 1998 default) · Tier 2
- IDT OligoAnalyzer — primer analysis and Tm tool · Tier 2
- NEB Tm Calculator · Tier 2
- Wikipedia — Nucleic acid thermodynamics · Tier 3
GC Content Calculator
Method: GC% = strong / length × 100; strong = G + C + S; weak = A + T + U + W · version 1.0 · reviewed 2026-09
DNA Molecular Weight Calculator
Method: MW(ss) = Σ(n_base × M_base) − 61.96; MW(ds) = MW(sense) + MW(antisense) · version 1.0 · reviewed 2026-09
- Wikipedia — Base pair (a DNA base pair is roughly 618 daltons) · Tier 3
- Wikipedia — Deoxyadenosine monophosphate (331.222 g/mol) · Tier 3
- Wikipedia — Deoxycytidine monophosphate (307.199 g/mol) · Tier 3
- Wikipedia — Deoxyguanosine monophosphate (347.224 g/mol) · Tier 3
- Wikipedia — Deoxythymidine monophosphate (322.209 g/mol) · Tier 3
DNA Concentration Calculator
Method: conc (µg/mL) = A260 × factor × dilution factor / path length (cm) · version 1.0 · reviewed 2026-09
PCR Master Mix Calculator
Method: V_add = C_final × V_total / C_stock; V_masterMix = V_total / fold; V_water = V_total − (V_masterMix + 2·V_primer + V_dNTP + V_template) · version 1.0 · reviewed 2026-09
qPCR Efficiency Calculator
Method: Cq = slope × log10(conc) + intercept; efficiency E = 10^(−1/slope) − 1; efficiency % = E × 100 · version 1.0 · reviewed 2026-09
Delta Delta Ct (2^-ΔΔCt) Calculator
Method: ΔCt = Ct(target) − Ct(reference); ΔΔCt = ΔCt(test) − ΔCt(control); fold change = 2^(−ΔΔCt); log2 fold change = −ΔΔCt · version 1.0 · reviewed 2026-09
Hemocytometer Cell Counting Calculator
Method: cells/mL = mean(count per large square) × dilution factor × 10⁴ · version 1.0 · reviewed 2026-09
Cell Viability Calculator (Trypan Blue)
Method: viability % = live / (live + dead) × 100 · version 1.0 · reviewed 2026-09
Cell Seeding Density Calculator
Method: cells/well = target density × growth area (cm²) [or = target density when quoted per well] · version 1.0 · reviewed 2026-09
Population Doubling Time Calculator
Method: Td = t / n, where n = log₂(Nₜ/N₀) = ln(Nₜ/N₀)/ln(2) · version 1.0 · reviewed 2026-09
CFU/mL Calculator (Colony Forming Units)
Method: CFU/mL = (mean colony count × dilution factor) / plated volume (mL) · version 1.0 · reviewed 2026-09
Protein Molecular Weight Calculator
Method: MW = Σ(n_residue × M_residue) + 18.0153 · version 1.0 · reviewed 2026-09
Protein Isoelectric Point (pI) Calculator
Method: Q(pH) = Σ_basic 1/(1+10^(pH−pKa)) − Σ_acidic 1/(1+10^(pKa−pH)); pI is the pH where Q = 0 · version 1.0 · reviewed 2026-09
Protein Concentration Calculator (A280)
Method: ε280 = n(Trp)·5500 + n(Tyr)·1490 + n(Cystine)·125; c(M) = A280·DF / (ε280·path); mg/mL = c·MW · version 1.0 · reviewed 2026-09
Ligation Ratio Calculator
Method: mass_insert = molar ratio × (size_insert / size_vector) × mass_vector · version 1.0 · reviewed 2026-09
Transformation Efficiency Calculator
Method: TE (CFU/µg) = colonies / µg_plated; µg_plated = (DNA_ng / 1000) × (plated volume / recovery volume) · version 1.0 · reviewed 2026-09
Plasmid Molecular Weight Calculator
Method: MW (g/mol) = length (bp) × 660 g/mol·bp · version 1.0 · reviewed 2026-09
Restriction Enzyme Site Finder
Method: linear: n cuts → n+1 fragments; circular: n cuts → n fragments (1 cut linearizes) · version 1.0 · reviewed 2026-09
Beer-Lambert Law Calculator
Method: A = ε · c · l · version 1.0 · reviewed 2026-10
Michaelis-Menten Calculator
Method: v = Vmax · [S] / (Km + [S]) · version 1.0 · reviewed 2026-10
- Wikipedia — Michaelis–Menten kinetics (equation, Km meaning, diffusion limitation) · Tier 3
- Wikipedia — Enzyme kinetics (rate constants, Vmax and kcat definitions) · Tier 3
- Wikipedia — Turnover number (kcat = Vmax / [E]t) · Tier 3
- Wikipedia — Specificity constant (kcat/Km and its diffusion-controlled upper limit) · Tier 3
- Wikipedia — Competitive inhibition (apparent Km rises, Vmax unchanged) · Tier 3
- Wikipedia — Non-competitive inhibition (Vmax falls, Km unchanged) · Tier 3
- Wikipedia — Uncompetitive inhibition (Km and Vmax fall by the same factor) · Tier 3
Buffer Calculator
Method: S = Kw/[H⁺] − [H⁺] + C·(⟨j⟩ − z₀), with ⟨j⟩ = Σ j·α_j and α_j ∝ Π Ka/i / [H⁺]^j · version 1.0 · reviewed 2026-10
- Wikipedia — Henderson–Hasselbalch equation (the ratio form this page compares against) · Tier 3
- Wikipedia — Buffer solution (capacity β = dn/dpH) · Tier 3
- Wikipedia — Self-ionization of water (pKw anchors at 0, 25, 50, 75 and 100 °C) · Tier 3
- Wikipedia — Acetic acid (pKa 4.756) and Sodium acetate (molar masses) · Tier 3
- Wikipedia — Citric acid (pKa1–3 3.13/4.76/6.39; anhydrous and monohydrate masses) · Tier 3
- Wikipedia — Phosphoric acid (ladder 2.16/7.20/12.32) and the sodium and potassium phosphate salt pages (molar masses incl. hydrates) · Tier 3
- Wikipedia — MES (buffer) (pKa 6.15, 195.2 g/mol) · Tier 3
- Wikipedia — PIPES (pKa 6.76 at 25 °C, second step 2.67, 302.37 g/mol) · Tier 3
- Wikipedia — MOPS (pKa 7.20, 209.26 g/mol) · Tier 3
- Wikipedia — HEPES (pKa1 3, pKa2 7.5, useful range 6.8–8.2, 238.3012 g/mol) · Tier 3
- Wikipedia — Tris (pKa 8.07 of the conjugate acid, 121.136 g/mol, and the −0.025 pH/°C coefficient between 25 and 37 °C) · Tier 3
- Wikipedia — Ammonium chloride (pKa 9.24 of NH4+, 53.49 g/mol) and Ammonia (17.031 g/mol) · Tier 3
- Wikipedia — Glycine (pKa 2.34 carboxyl, 9.6 amino; 75.067 g/mol) · Tier 3
- Wikipedia — Good’s buffers (the sulfonate ladder framing for MES, MOPS, PIPES and HEPES) · Tier 3
- Wikipedia — Sodium hydroxide (39.997 g/mol) and Hydrochloric acid (36.46 g/mol) for titrant mass · Tier 3
OD600 Calculator
Method: cells/mL = (OD600_sample − OD600_blank) × factor × dilution factor · version 1.0 · reviewed 2026-10
- BioNumbers BNID 100985 — E. coli 1×10⁸ cells/mL at OD600 0.1 (Ausubel, Short Protocols 5th ed. Vol. 1) · Tier 2
- BioNumbers BNID 103625 — E. coli in LB 2×10⁷ cells/mL at OD600 0.1 (Sezonov 2007) · Tier 2
- BioNumbers BNID 100986 — S. cerevisiae 3×10⁷ cells/mL at OD600 1, with the “measure below OD 1” comment · Tier 2
- BioNumbers BNID 106301, 106300, 106299 — S. cerevisiae stationary phase at 30, 20 and 10 °C (Margesin 2009) · Tier 2
- BioNumbers BNID 105287 — B. subtilis 5×10⁸ cells/mL at OD600 1 (Fisher 2001) · Tier 2
- BioNumbers BNID 105286 — B. subtilis 1×10⁷–5×10⁷ cells/mL at OD600 ~0.1, published as a range (Arrieta 2006) · Tier 2
- BioNumbers BNID 109838, 109835, 109837, 107924 — E. coli g DCW/L per OD600: 0.33, 0.30, 0.36, 0.47 · Tier 2
- BioNumbers BNID 108275 — S. pombe 1 OD600 = 0.62 g DCW/L (Sohn 2012) · Tier 2
- BioNumbers BNID 109702 — C. glutamicum 5.5 g CDW/L at OD600 15 and 9.6 at OD30, the high-density flattening (Noack 2011) · Tier 2
- BioNumbers BNID 106303 — maximum OD600 of S. cerevisiae in YPD, 5.2 ± 0.2 (Boccazzi 2006) · Tier 2
- Sezonov G et al. Escherichia coli physiology in Luria-Bertani broth. J Bacteriol 2007;189:8746-9 · Tier 1
- Day AC, Schneider C, Schneider BL. Yeast cell synchronization. Methods Mol Biol 2004;241:55-76 · Tier 1
- Margesin R. Effect of temperature on growth parameters of psychrophilic bacteria and yeasts. Extremophiles 2009;13:257-62 · Tier 1
- Fisher AJ et al. Nonradioactive assay for cellular dimethylallyl diphosphate. Anal Biochem 2001;292:272-9 · Tier 1
- Arrieta MC, Leskiw BK, Kaufman WR. Exp Appl Acarol 2006;39:297-313 · Tier 1
- Sauer U et al. J Bacteriol 1999;181:6679-88 (E. coli OD600 → 0.33 g/L dry weight) · Tier 1
- Soini J, Ukkonen K, Neubauer P. Microb Cell Fact 2008;7:26 (E. coli W3110, 0.3 g/L per OD600) · Tier 1
- Ren Q et al. BMC Biotechnol 2013;13:18 (E. coli cdw/OD = 0.36) · Tier 1
- Akhtar MK, Jones PR. Metab Eng 2009;11:139-47 (BL21(DE3) 0.47 ± 0.03 g DCW/L per OD600) · Tier 1
- Noack S et al. J Biotechnol 2011;154:179-90 (C. glutamicum dry weight at OD600 15 and 30) · Tier 1
- BioNumbers — the curated physiology database behind every factor on this page (Milo lab, Harvard) · Tier 2
Hardy-Weinberg Calculator
Method: p = (2·nAA + nAa) / 2N; q = 1 − p, and for k alleles pᵢ = (2·nᵢᵢ + Σᵢ≠ⱼ nᵢⱼ) / 2N · version 1.0 · reviewed 2026-10
- Wikipedia — Hardy–Weinberg principle (the (p + q)² derivation, the chi-square test with its degrees-of-freedom rule, F = 1 − Ho/He, the conditional exact distribution, and the X-linked expectation) · Tier 3
- Wikipedia — Binomial proportion confidence interval (the Wilson score interval used for the allele frequency) · Tier 3
- Wikipedia — Fisher's exact test (why a chi-square needs large expected cell counts, and the usual 5 and 10 thresholds) · Tier 3
- Wikipedia — Pearson's chi-squared test (df = categories − parameters, and the right-tail p-value) · Tier 3
Punnett Square Calculator
Method: P(zygote) = Σ over the two gametes of P(gamete from parent 1) × P(gamete from parent 2), over 4^L equally likely zygotes · version 1.0 · reviewed 2026-10
- StatPearls — Genetics: Inheritance Patterns (autosomal, X-linked and mitochondrial patterns and their risks to offspring) · Tier 1
- Wikipedia — Punnett square (the square construction and its gamete assumptions) · Tier 3
- Wikipedia — Test cross (why a homozygous recessive partner reads gametes straight off the offspring) · Tier 3
- Wikipedia — Genetic linkage (recombination fraction, coupling and repulsion, centiMorgans) · Tier 3
Standing reference libraries
Beyond the tool-specific citations above, these are the primary libraries we consult when adding a new calculator or checking a constant:
- NIST Chemistry WebBook · Tier 1
- NCBI — National Center for Biotechnology Information · Tier 1
- PubMed · Tier 1
- NEB NEBioCalculator · Tier 2
- Promega Biomath Tools · Tier 2
- IDT OligoAnalyzer · Tier 2
- Thermo Fisher Scientific · Tier 2
If a reference looks wrong
Citations are checked before a tool goes live, but science moves and links change. If a source no longer supports the claim it backs, or you know a better primary reference, send the page URL and the correction to us via the contact page. We review every report and update the citation when warranted.