Science Formula Reference Guide — Physics, Chemistry, Math & Biology

I'm the founder of SciSolveLab (scisolvelab.com), a free collection of science calculators covering physics, chemistry, mathematics, and biology — built specifically for students and researchers.

Your readers regularly engage with articles covering topics like kinetic energy, molarity, pH, ideal gas law, and unit conversions. SciSolveLab offers free, instant calculators for all of these — no login, no ads, works on any device.
WEBSITE
https://scisolvelab.com

I'd love to suggest scisolvelab.com as a resource link on relevant topic pages or your tools/resources section, if one exists. Many of your articles explain the science beautifully — our calculators let readers immediately apply those concepts without leaving the learning flow.

Transcript

1. s Science Formula Reference Guide Physics · Chemistry · Mathematics · Biology Free interactive calculators at scisolvelab.com s PHYSICS ss CHEMISTRY s MATHEMATICS s BIOLOGY This reference guide contains the most commonly used formulas across four core science subjects. Use it alongside the free interactive calculators at scisolvelab.com — plug in your values and get instant, accurate results with automatic unit conversion. No login required. Works on any device. s All formulas in this guide have a free calculator at scisolvelab.com Section Formulas covered Page 1. Physics Kinetic energy, force, velocity, momentum, waves, gravity 2 2. Chemistry Molarity, pH, ideal gas law, concentration, stoichiometry 3 3. Mathematics Statistics, unit conversion, algebra, geometry 4 4. Biology Population growth, BMI, genetics, metabolic rate 5 5. Constants Universal constants and SI unit reference 6
2. SciSolveLab — Science Formula Reference Guide scisolvelab.com | Page 2 s Section 1 — Physics Formulas 1.1 Mechanics Kinetic Energy KE = ½ × m × v² m = mass (kg), v = velocity (m/s), KE in Joules Potential Energy PE = m × g × h g = 9.81 m/s², h = height (m), PE in Joules Newton's 2nd Law F = m × a F = force (N), m = mass (kg), a = acceleration (m/s²) Work Done W = F × d × cos θ F = force (N), d = displacement (m), θ = angle Power P = W ÷ t P = power (W), W = work (J), t = time (s) Momentum p = m × v p = momentum (kg·m/s), m = mass, v = velocity Impulse J = F × ∆t J = impulse (N·s), F = force, ∆t = time interval 1.2 Kinematics (SUVAT) Velocity v = u + at u = initial velocity, a = acceleration, t = time Displacement s = ut + ½at² s = displacement (m) Velocity squared v² = u² + 2as Useful when time is unknown Average velocity s = ½(u + v) × t Mean of initial and final velocity × time 1.3 Waves & Gravity Wave Speed v = f × λ f = frequency (Hz), λ = wavelength (m) Period T = 1 ÷ f T = period (s), f = frequency (Hz) Gravitational PE GPE = mgh Same as potential energy — m, g, h Centripetal Force F = mv² ÷ r r = radius of circular path (m) s Use free physics calculators at scisolvelab.com — kinetic energy, force, velocity, waves & more
3. SciSolveLab — Science Formula Reference Guide scisolvelab.com | Page 3 ss Section 2 — Chemistry Formulas 2.1 Solutions & Concentration Molarity M = n ÷ V n = moles of solute, V = volume of solution (L) Moles from mass n = m ÷ Mr m = mass (g), Mr = molar mass (g/mol) Dilution CsVs = CsVs Concentration × volume before = after dilution Mass from moles m = n × Mr m = mass (g), n = moles, Mr = molar mass Concentration c = m ÷ (Mr × V) Direct formula combining mass, molar mass, volume 2.2 Acids, Bases & pH pH pH = -log[Hs] [Hs] = hydrogen ion concentration (mol/L) pOH pOH = -log[OHs] [OHs] = hydroxide ion concentration (mol/L) pH + pOH pH + pOH = 14 At 25°C in aqueous solution Hs from pH [Hs] = 10sss Reverse of pH formula Ka (acid constant) Ka = [Hs][As] ÷ [HA] Equilibrium constant for weak acid dissociation 2.3 Gases & Thermodynamics Ideal Gas Law PV = nRT R = 8.314 J/mol·K | T must be in Kelvin Celsius to Kelvin K = °C + 273.15 Always convert temperature before using PV=nRT Boyle's Law PsVs = PsVs Constant temperature — pressure × volume Charles's Law Vs÷Ts = Vs÷Ts Constant pressure — volume proportional to T Combined Gas Law PsVs÷Ts = PsVs÷Ts Combines Boyle's and Charles's Laws s Free chemistry calculators at scisolvelab.com — molarity, pH, ideal gas law & more
4. SciSolveLab — Science Formula Reference Guide scisolvelab.com | Page 4 s Section 3 — Mathematics Formulas 3.1 Statistics Mean (average) µ = Σx ÷ N Sum of all values divided by count Variance σ² = Σ(x-µ)² ÷ N Average of squared differences from mean Std Deviation σ = √(Σ(x-µ)² ÷ N) Square root of variance Probability P(A) = favourable ÷ total Number of favourable outcomes ÷ total Median Middle value of sorted data If even count: average of two middle values 3.2 Algebra & Equations Quadratic Formula x = (-b ± √(b²-4ac)) ÷ 2a For ax² + bx + c = 0 Discriminant ∆ = b² - 4ac ∆>0: two roots, ∆=0: one root, ∆<0: no real roots Slope of line m = (ys-ys) ÷ (xs-xs) Rise over run between two points Line equation y = mx + c m = slope, c = y-intercept 3.3 Geometry Circle area A = π × r² r = radius Circle circumference C = 2πr r = radius Sphere volume V = (4÷3) × π × r³ r = radius Pythagoras a² + b² = c² c = hypotenuse of right-angled triangle Triangle area A = ½ × b × h b = base, h = perpendicular height s Free math calculators at scisolvelab.com — statistics, unit conversion, algebra & more
5. SciSolveLab — Science Formula Reference Guide scisolvelab.com | Page 5 s Section 4 — Biology Formulas 4.1 Human Biology BMI BMI = weight(kg) ÷ height(m)² Under 18.5 = underweight, 18.5–24.9 = normal BMR (Mifflin-St Jeor) Men: 10m + 6.25h - 5a + 5 m=kg, h=cm, a=age | Women: use -161 not +5 Heart Rate Max HRmax = 220 - age Estimated maximum heart rate by age Target Heart Rate THR = HRmax × 0.5–0.85 50–85% of max heart rate for exercise zones 4.2 Population & Growth Population Growth N(t) = Ns × e^(rt) Ns = initial pop, r = growth rate, t = time Doubling Time t = ln(2) ÷ r r = growth rate; ln(2) ≈ 0.693 Growth Rate r = (Births - Deaths) ÷ N Per capita rate of increase Carrying Capacity dN/dt = rN(1 - N/K) K = carrying capacity (logistic growth) 4.3 Genetics Hardy-Weinberg p² + 2pq + q² = 1 p = dominant allele freq, q = recessive allele freq Allele frequencies p + q = 1 Sum of all allele frequencies = 1 Expected heterozygotes 2pq Frequency of heterozygous individuals in population s Free biology calculators at scisolvelab.com — BMI, population growth, genetics & more
6. SciSolveLab — Science Formula Reference Guide scisolvelab.com | Page 6 s Section 5 — Universal Constants & Unit Reference 5.1 Physical Constants Constant Symbol Value Unit Speed of light c 2.998 × 10s m/s Gravitational constant G 6.674 × 10s¹¹ N·m²/kg² Planck's constant h 6.626 × 10s³s J·s Avogadro's number Ns 6.022 × 10²³ mols¹ Gas constant R 8.314 J/mol·K Boltzmann constant kB 1.381 × 10s²³ J/K Elementary charge e 1.602 × 10s¹s C Electron mass me 9.109 × 10s³¹ kg Standard gravity g 9.807 m/s² Atmospheric pressure atm 101,325 Pa 5.2 Common Unit Conversions From To Multiply by Category kilometres (km) metres (m) × 1,000 Length miles kilometres × 1.609 Length kilograms (kg) grams (g) × 1,000 Mass pounds (lb) kilograms (kg) × 0.4536 Mass °Celsius Kelvin (K) + 273.15 Temperature °Fahrenheit °Celsius (F-32) × 5/9 Temperature litres (L) millilitres (mL) × 1,000 Volume atmospheres (atm) Pascals (Pa) × 101,325 Pressure electronvolts (eV) Joules (J) × 1.602×10s¹s Energy calories (cal) Joules (J) × 4.184 Energy s Unit conversion calculator at scisolvelab.com — handles all major science units automatically
7. SciSolveLab — Science Formula Reference Guide scisolvelab.com | Page 7 s Try All These Formulas Live Every formula in this guide has a free interactive calculator at scisolvelab.com — just enter your values and get instant results. scisolvelab.com Free · No login · Works on any device © SciSolveLab — scisolvelab.com · Free to share and distribute for educational purposes