Half-life / first-order decay API

Relates rate constant k and half-life, then computes remaining fraction/amount after time t or the time to reach a target fraction via N(t)=N0·e^(-kt). Answers 'How much remains after two half-lives?', 'What is k for a given half-life?', 'carbon-14 dating fraction'.

Price$0.06per request

MethodPOST

Route/v1/chemistry/first-order-kinetics

StatusLive

MIME typeapplication/json

Rate limit120/minute

Cache0s public

chemistrykineticshalf-lifefirst-orderdecayrate-constantradioactiveexponential

API URLhttps://x402.hexl.dev/v1/chemistry/first-order-kinetics

Integration docs

Example request

{
  "halfLife": 5730,
  "time": 11460,
  "initialAmount": 100
}

Example response

{
  "rateConstant": 0.0001209681,
  "halfLife": 5730,
  "formula": "N(t) = N0·e^(-kt); t½ = ln2 / k",
  "time": 11460,
  "remainingFraction": 0.25,
  "percentRemaining": 25,
  "halfLivesElapsed": 2,
  "remainingAmount": 25
}

Input schema

{
  "type": "object",
  "properties": {
    "halfLife": {
      "type": "number",
      "examples": [
        5730
      ]
    },
    "rateConstant": {
      "type": "number"
    },
    "time": {
      "type": "number",
      "examples": [
        11460
      ]
    },
    "initialAmount": {
      "type": "number",
      "examples": [
        100
      ]
    },
    "remainingFraction": {
      "type": "number"
    }
  }
}

Output schema

{
  "type": "object",
  "additionalProperties": true
}