Physics, chemistry and biology formulas: velocity, electric field, resistance, growth, cell density
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Calculates bacterial population after a given time using exponential growth formula: N(t) = N₀ × e^(rt) or N(t) = N₀ × 2^(t/doubling_time). (cost: 1 credit)
number, required, time elapsed, hours, no default
number, optional, exponential growth rate, per hour, no default
number, optional, population doubling time, hours, no default
number, required, starting population size, cells, no default
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Authorization (optional, not in the config above): Optional. Bearer <key> for more than the free daily allowance; free key from POST https://ukdata.reliness.co.uk/keysCalculates bacterial population after a given time using exponential growth formula: N(t) = N₀ × e^(rt) or N(t) = N₀ × 2^(t/doubling_time). (cost: 1 credit)
| Argument | Type | Description |
|---|---|---|
| time | number | string | number, required, time elapsed, hours, no default |
| growth_rate | number | string | number, optional, exponential growth rate, per hour, no default |
| doubling_time | number | string | number, optional, population doubling time, hours, no default |
| initial_population | number | string | number, required, starting population size, cells, no default |
{
"type": "object",
"$schema": "http://json-schema.org/draft-07/schema#",
"properties": {
"time": {
"type": [
"number",
"string"
],
"description": "number, required, time elapsed, hours, no default"
},
"growth_rate": {
"type": [
"number",
"string"
],
"description": "number, optional, exponential growth rate, per hour, no default"
},
"doubling_time": {
"type": [
"number",
"string"
],
"description": "number, optional, population doubling time, hours, no default"
},
"initial_population": {
"type": [
"number",
"string"
],
"description": "number, required, starting population size, cells, no default"
}
}
}Calculates cell density (cells per mL) from optical density (OD) measurement and dilution factor. Formula: OD × dilution × factor (default 1e9 cells/mL per OD unit, organism-dependent). (cost: 1 credit)
| Argument | Type | Description |
|---|---|---|
| od | number | string | number, required, optical density measurement, absorbance units, no default |
| factor | number | string | number, optional, cells/mL per OD unit, default 1e9 |
| dilution | number | string | number, required, dilution factor, fold dilution, no default |
{
"type": "object",
"$schema": "http://json-schema.org/draft-07/schema#",
"properties": {
"od": {
"type": [
"number",
"string"
],
"description": "number, required, optical density measurement, absorbance units, no default"
},
"factor": {
"type": [
"number",
"string"
],
"description": "number, optional, cells/mL per OD unit, default 1e9"
},
"dilution": {
"type": [
"number",
"string"
],
"description": "number, required, dilution factor, fold dilution, no default"
}
}
}Calculates the electric field strength produced by a point charge at a given distance using Coulomb's law: E = kQ/r². Uses permittivity parameter or defaults to vacuum permittivity. (cost: 1 credit)
| Argument | Type | Description |
|---|---|---|
| charge | number | string | number, required, electric charge in coulombs (C) |
| distance | number | string | number, required, distance from the charge in meters (m) |
| permitivity | number | string | number, optional, permittivity of the medium in F/m, default 8.854e-12 (vacuum) |
{
"type": "object",
"$schema": "http://json-schema.org/draft-07/schema#",
"properties": {
"charge": {
"type": [
"number",
"string"
],
"description": "number, required, electric charge in coulombs (C)"
},
"distance": {
"type": [
"number",
"string"
],
"description": "number, required, distance from the charge in meters (m)"
},
"permitivity": {
"type": [
"number",
"string"
],
"description": "number, optional, permittivity of the medium in F/m, default 8.854e-12 (vacuum)"
}
}
}Calculates final velocity using the kinematic equation: v = v₀ + at, where v₀ is initial velocity, a is acceleration, and t is time. (cost: 1 credit)
| Argument | Type | Description |
|---|---|---|
| time | number | string | number, required, time elapsed, seconds, no default |
| acceleration | number | string | number, required, acceleration, meters per second squared, no default |
| initial_velocity | number | string | number, required, starting velocity, meters per second, no default |
{
"type": "object",
"$schema": "http://json-schema.org/draft-07/schema#",
"properties": {
"time": {
"type": [
"number",
"string"
],
"description": "number, required, time elapsed, seconds, no default"
},
"acceleration": {
"type": [
"number",
"string"
],
"description": "number, required, acceleration, meters per second squared, no default"
},
"initial_velocity": {
"type": [
"number",
"string"
],
"description": "number, required, starting velocity, meters per second, no default"
}
}
}Calculates electrostatic potential energy using the formula U = qV, where U is energy, q is charge, and V is voltage. (cost: 1 credit)
| Argument | Type | Description |
|---|---|---|
| charge | number | string | number, required, electric charge, coulombs (C), no default |
| voltage | number | string | number, required, electric potential difference, volts (V), no default |
{
"type": "object",
"$schema": "http://json-schema.org/draft-07/schema#",
"properties": {
"charge": {
"type": [
"number",
"string"
],
"description": "number, required, electric charge, coulombs (C), no default"
},
"voltage": {
"type": [
"number",
"string"
],
"description": "number, required, electric potential difference, volts (V), no default"
}
}
}Projects future population size using exponential growth formula with a constant annual growth rate (percentage). (cost: 1 credit)
| Argument | Type | Description |
|---|---|---|
| num_years | number | string | number, required, number of years to project forward |
| current_pop | number | string | number, required, the current population size |
| annual_growth | number | string | number, required, annual growth rate as a percentage (e.g., 2.5 for 2.5%) |
{
"type": "object",
"$schema": "http://json-schema.org/draft-07/schema#",
"properties": {
"num_years": {
"type": [
"number",
"string"
],
"description": "number, required, number of years to project forward"
},
"current_pop": {
"type": [
"number",
"string"
],
"description": "number, required, the current population size"
},
"annual_growth": {
"type": [
"number",
"string"
],
"description": "number, required, annual growth rate as a percentage (e.g., 2.5 for 2.5%)"
}
}
}Calculates electrical resistance of a wire using the formula R = ρL/A, where R is resistance, ρ is material resistivity, L is length, and A is cross-sectional area. (cost: 1 credit)
| Argument | Type | Description |
|---|---|---|
| length_m | number | string | number, required, length of the wire, meters (m), no default |
| material | string | string, required, material type (e.g., copper, aluminum, silver, gold), no units, no default |
| area_sq_m | number | string | number, required, cross-sectional area of the wire, square meters (m²), no default |
{
"type": "object",
"$schema": "http://json-schema.org/draft-07/schema#",
"properties": {
"length_m": {
"type": [
"number",
"string"
],
"description": "number, required, length of the wire, meters (m), no default"
},
"material": {
"type": "string",
"description": "string, required, material type (e.g., copper, aluminum, silver, gold), no units, no default"
},
"area_sq_m": {
"type": [
"number",
"string"
],
"description": "number, required, cross-sectional area of the wire, square meters (m²), no default"
}
}
}We read every tool's name, description and inputs the way the model will, looking for instructions hidden from you. A clean result means no warning signs, not a guarantee. Scanned Nov 7, 2026.