Shear modulus calculator

What shear modulus means: G = τ / γ

Shear stress has the same dimensions as normal stress: force parallel to the surface divided by the area of that surface, so when force is in newtons and area is in square metres, tau is in pascals. Because gamma has no unit, G inherits the unit of tau; this endpoint always reports shear_modulus in pascals and also reports shear_modulus_gpa as that value divided by one billion, matching the gigapascal columns in almost every metal handbook. The path is deterministic floating-point arithmetic with fixed precision rounding so Worker and browser JSON match byte for byte on every identical call.

How to call the API and what comes back

Signed stress and strain are allowed so engineering sign conventions survive the round trip; G then inherits the sign of the quotient. There is no material table, no temperature correction, no unit converter from megapascals or microstrain, and no rearrangement that solves for a missing tau or gamma. POST a JSON body with two required finite numbers: shear_stress (aliases tau and stress) in pascals, and shear_strain (aliases gamma and strain), which is dimensionless. Each field may arrive as a JSON number or as a numeric string from a form; missing fields, empty strings, non-numeric text, NaN, and Infinity fail immediately with invalid_input naming the field, and those failures are never charged. After both values parse, shear strain is checked against a hard physical bound: if its absolute value is zero or no larger than one times ten to the minus fifteen, the task fails with invalid_input and a message that shear modulus G equals tau over gamma is undefined when shear_strain is zero. That near-zero floor stops floating noise from inventing an absurdly large modulus. On success the response echoes rounded shear_stress and shear_strain, sets shear_modulus to the rounded quotient in pascals, sets shear_modulus_gpa to that modulus divided by one billion, sets unit to Pa, sets formula to the string G equals tau over gamma, and sets method to shear_modulus so clients can branch without sniffing shapes. Pricing is a flat $0.002 per successful request with unit item.

Practical tips, units, and related searches

Keep shear stress and shear strain inside the published absolute range so the quotient cannot overflow into a non-finite modulus the solver must reject. Use consistent SI interpretation: pascals for tau yield pascals for G; if your lab sheet lists megapascals or pounds per square inch, convert first—this tool does not convert units. Engineering shear strain is not a percentage: a half-percent shear is 0.005, not 0.5, and mixing those scales is the most common source of a modulus that looks a hundred times too small. Prefer this capability when you already have shear stress and shear strain and only need G in pascals. Prefer sending JSON numbers rather than pre-formatted strings when you control the client. When teaching, pair examples: eighty million pascals of shear at one thousandth strain recovers eighty gigapascals, a familiar steel-class rigidity, and a deliberate zero strain demonstrates the hard invalid_input path. This landing targets people searching for a shear modulus calculator, modulus of rigidity calculator, or G equals tau over gamma online. It is not Young's modulus E equals sigma over epsilon, not average shear stress tau equals F over A, not transverse beam shear VQ over It, and not a finite-element solver. Failed tasks that return invalid_input do not consume prepaid balance, which keeps exploratory scripts cheap when learners deliberately send a zero strain. Round-trip checks are easy: recompute tau divided by gamma by hand and confirm it equals the published shear_modulus within the same rounding, and confirm that zero strain always fails with invalid_input mentioning that shear strain is zero. Each successful API call is one billable item at $0.002.