Biophysics Calculators
Free biophysics calculators: Nernst potential, Stokes-Einstein diffusion coefficient, and Michaelis-Menten enzyme kinetics for cell physiology and biochemistry.
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.
Three Biophysics Calculators
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.
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.