Half-Life Calculator
This calculator helps you determine the half-life of a substance given its first-order rate constant. Half-life is the time required for a quantity to reduce to half of its initial value. It is a fundamental concept in nuclear physics, chemistry, and pharmacology.
For a first-order reaction, the relationship between the half-life ($t_{1/2}$) and the rate constant ($k$) is given by the formula:
$t_{1/2} = \frac{\ln(2)}{k}$
Where:
- $t_{1/2}$ is the half-life (typically in seconds, minutes, hours, or days).
- $k$ is the first-order rate constant (with units inverse to time, e.g., s⁻¹, min⁻¹, h⁻¹, day⁻¹).
- $\ln(2)$ is the natural logarithm of 2, which is approximately 0.693.
Ensure that the units of your rate constant are consistent with the desired units for your half-life calculation.
per second (s⁻¹)
per minute (min⁻¹)
per hour (hr⁻¹)
per day (day⁻¹)
function calculateHalfLife() {
var rateConstantInput = document.getElementById("rateConstant");
var rateUnitSelect = document.getElementById("rateUnit");
var resultDiv = document.getElementById("result");
var k = parseFloat(rateConstantInput.value);
var selectedUnit = rateUnitSelect.value;
if (isNaN(k) || k <= 0) {
resultDiv.innerHTML = "Please enter a valid positive number for the rate constant.";
return;
}
var ln2 = Math.log(2);
var halfLife = ln2 / k;
var unitLabel = "";
if (selectedUnit === "s") {
unitLabel = "seconds";
} else if (selectedUnit === "min") {
unitLabel = "minutes";
} else if (selectedUnit === "hr") {
unitLabel = "hours";
} else if (selectedUnit === "day") {
unitLabel = "days";
}
resultDiv.innerHTML = "The half-life is: " + halfLife.toFixed(4) + " " + unitLabel;
}