Biophysics Calculators
Free biophysics calculators: Nernst potential, GHK equation, diffusion and crowding, FRET, worm-like chain, sedimentation, and enzyme kinetics.
Biophysics Calculators - Cell Physiology and Molecular Biophysics
Biophysics sits at the intersection of physics, chemistry, and biology, applying quantitative physical laws to living systems: how ions cross cell membranes to generate electrical signals, how molecules diffuse through crowded cellular environments, and how enzymes speed up the chemical reactions that sustain life. These calculators cover foundational formulas used across neuroscience, molecular biology, and biochemistry coursework and research.
Twenty-Six Biophysics Calculators
The Cable Equation Axon Length Constant Calculator finds a neuron’s electrotonic space constant lambda from membrane resistivity, axial resistivity, and axon diameter, with an interactive chart showing the square-root scaling of lambda with diameter. The Protein Folding Free Energy Estimator finds a protein’s folding stability (dG = dH - TdS) and melting temperature from the enthalpy and entropy change of folding, with the dG-versus-temperature curve plotted and the melting-temperature crossing marked. The Hydrophobicity Scale and Transfer Free Energy Calculator looks up the Kyte-Doolittle hydropathy index and Fauchere-Pliska transfer free energy for every residue in a typed amino acid sequence, with a residue-by-residue breakdown table. The Goldman-Hodgkin-Katz Equation Calculator finds a cell’s resting membrane potential from the relative permeabilities and concentrations of K+, Na+, and Cl- together, with an interactive chart of Vm versus Na+ permeability showing the shift from a K+-dominated resting potential toward a Na+-dominated depolarized state. The Action Potential Threshold Estimator classifies an injected current as subthreshold or suprathreshold using a passive RC membrane model and computes the exact time to reach firing threshold, with the membrane voltage charging curve plotted against the threshold line. The Hodgkin-Huxley Conductance Calculator finds instantaneous Na+ and K+ conductance from the classic gNa=gNaBar m³h and gK=gKBar n⁴ gating-variable formulas, plus the resulting ionic currents, with the steep cubic and quartic conductance curves plotted. The Nernst Potential Calculator finds the equilibrium electrochemical potential for a single ion species across a cell membrane, verified against real potassium, sodium, and chloride resting-potential values - the same equation that underlies the Goldman-Hodgkin-Katz treatment of the neuronal resting potential and action potential. The Diffusion Coefficient (Einstein-Stokes) Calculator finds a spherical particle’s translational diffusion coefficient from its hydrodynamic radius, the medium’s temperature, and viscosity, with an interactive D-versus-radius chart showing why large proteins diffuse far more slowly than small ions. The Enzyme Kinetics (Michaelis-Menten) Calculator finds enzyme reaction velocity and percent saturation from Vmax, Km, and substrate concentration, with the classic saturation curve plotted and the Km half-saturation point marked - Km is the substrate concentration at which the reaction runs at exactly half its maximum rate. The Membrane Capacitance and Time Constant Calculator finds a cell membrane’s electrical time constant (tau = Rm x Cm) and cutoff frequency from its resistance and capacitance, with the classic RC charging curve plotted and the one-tau (63.2%) point marked. The Osmotic Pressure Calculator finds the osmotic pressure a solute exerts across a semipermeable biological membrane using the van’t Hoff equation (pi = iMRT), verified against real physiological plasma osmotic pressure. The ATP Hydrolysis Free Energy Calculator finds the actual free energy released by ATP hydrolysis under real cellular concentrations (dG = dG0’ + RT·ln([ADP][Pi]/[ATP])), showing why physiological conditions release substantially more energy than the standard-state textbook value.
Fourteen further calculators extend the collection from cell physiology into molecular and sensory biophysics. The Fick Law Membrane Diffusion Calculator finds the steady-state flux, permeability coefficient, and transport rate across a membrane from the diffusion coefficient, partition coefficient, and thickness, with a diagram of the concentration drop across the bilayer. The Sedimentation Coefficient (Svedberg) Calculator converts boundary movement in an analytical ultracentrifuge into svedberg units and, through the Svedberg equation, into molar mass. The Buoyant Force on Macromolecule Calculator separates the weight, buoyant force, and net sedimenting force acting on one molecule, and marks the solvent density at which a molecule becomes neutrally buoyant and stops sedimenting altogether. The FRET Efficiency and Forster Radius Calculator converts in three directions between energy transfer efficiency, donor-acceptor separation, and the Forster radius derived from spectral overlap, with the steep sixth-power distance dependence plotted in every mode.
On the mechanics side, the Single Molecule Force Spectroscopy (WLC) Calculator applies the Marko-Siggia interpolation formula to find the entropic restoring force and local stiffness of a stretched biopolymer, the regime probed by optical tweezers and AFM pulling experiments. The Bending Stiffness of Lipid Bilayer Calculator converts an area compressibility modulus and hydrocarbon thickness into a bending modulus in both zeptojoules and units of kBT, across the three standard monolayer coupling models. The Membrane Tension and Laplace Pressure Calculator applies the Young-Laplace relation to vesicles, soap bubbles, and cylindrical tubes, and warns when the resulting areal strain exceeds the bilayer lysis threshold. The Crowding Effect on Diffusion Calculator estimates how severely macromolecular crowding slows a tracer inside a real cell, comparing stretched exponential, Muramatsu-Minton, and obstruction-scaling models side by side. The Muscle Force-Velocity (Hill Equation) Calculator plots A. V. Hill’s classic hyperbola and identifies the intermediate load at which a muscle delivers peak mechanical power.
Four more cover nucleic acids, light, and ligand binding. The DNA Persistence Length and Contour Calculator turns a length in base pairs into contour length, root-mean-square end-to-end distance, radius of gyration, and Kuhn segment count, showing where a molecule sits between the rigid-rod and random-coil regimes. The RNA Secondary Structure Melting Temperature Calculator sums published nearest-neighbor stacking parameters over a typed sequence to predict melting temperature and folding free energy, with a salt correction and a per-step thermodynamics table. The Vision Photon Catch Rate Calculator works out how many photons a single rod or cone absorbs each second from scene radiance, pupil diameter, and ocular transmittance, and reports the Poisson probability of catching at least one photon in a given integration time. The Cooperative Binding (Hill Equation) Calculator finds fractional occupancy for a cooperative receptor and classifies the Hill coefficient as positive, negative, or non-cooperative, the relationship behind the sigmoidal oxygen-hemoglobin binding curve. The Fluorescence Lifetime and Quantum Yield Calculator links lifetime, quantum yield, and the radiative and non-radiative decay rate constants, and supports the comparative method for measuring quantum yield against a reference standard.
Who Uses These Calculators
Undergraduate and graduate students in biophysics, physiology, and molecular biology use these tools for problem-set verification in cell physiology and biochemistry coursework. Neuroscience students use the Nernst Potential Calculator to build intuition for resting and action potentials before tackling the full Hodgkin-Huxley model. Biochemistry and pharmacology students use the Michaelis-Menten calculator to interpret enzyme assay data and drug-receptor kinetics. Researchers modeling protein or nanoparticle transport in solution use the Einstein-Stokes calculator for quick order-of-magnitude diffusion estimates before running full molecular dynamics simulations.
Constants Behind Biophysics
The gas constant R = 8.314 J/(mol·K) and Faraday’s constant F = 96,485 C/mol together set the scale of every ionic equilibrium potential calculated here. The Boltzmann constant k = 1.380649×10⁻²³ J/K sets the scale of thermal (Brownian) motion behind molecular diffusion. Human body temperature, 37°C (310.15 K), is the default temperature used throughout, since it is the physiologically relevant value for mammalian cell biophysics.
Frequently Asked Questions
What is biophysics?
Biophysics is the science of applying the principles and quantitative methods of physics and physical chemistry to biological systems, from the electrical behavior of a single cell membrane to the diffusion of a protein through the cytoplasm. The Nernst Potential Calculator and Diffusion Coefficient Calculator on this page both apply classic biophysical equations to real physiological and molecular examples.
Why does cell physiology rely so heavily on equations from physics and chemistry?
A cell's electrical signaling, ion transport, and molecular transport are all governed by the same physical laws that describe ions and molecules anywhere, the Nernst equation, Fick's law of diffusion, and the Stokes-Einstein relation. What makes biophysics distinct is applying these general physical laws to the specific, measurable quantities found in living cells, such as ion concentration gradients and enzyme reaction rates.
Why is the resting potential of a neuron close to the potassium Nernst potential?
A resting neuron's membrane is far more permeable to K⁺ than to Na⁺ or Cl⁻, so the Goldman-Hodgkin-Katz equation (a permeability-weighted extension of the Nernst equation) is dominated by the potassium term. With typical mammalian concentrations ([K⁺]in ≈ 140 mM, [K⁺]out ≈ 5 mM), the Nernst Potential Calculator gives E_K ≈ −90 mV at 37°C, close to the typical measured resting potential of −70 mV; the gap is explained by the smaller but non-zero Na⁺ and Cl⁻ permeabilities.
What does the Michaelis constant Km actually mean?
Km is the substrate concentration at which an enzyme-catalyzed reaction proceeds at exactly half its maximum velocity (Vmax/2). A low Km means the enzyme reaches near-maximum speed at low substrate concentration, indicating high substrate affinity; a high Km means more substrate is needed to saturate the enzyme. The Enzyme Kinetics Calculator marks this half-saturation point directly on the plotted curve.
Why do larger molecules diffuse more slowly?
The Stokes-Einstein relation D = kT/(6πηr) puts the hydrodynamic radius r in the denominator, so diffusion coefficient falls off inversely with particle size - a protein with 10 times the radius of a small ion diffuses roughly 10 times slower at the same temperature and viscosity. This is why large proteins and organelles rely on active transport rather than diffusion alone to move any meaningful distance inside a cell. The Diffusion Coefficient Calculator plots this relationship directly.