Decay Constant Calculator
Calculate decay constant with our free science calculator. Uses standard scientific formulas with unit conversions and explanations.
Calculator
Adjust values & calculateFormula
The decay constant equals the natural logarithm of 2 (0.693147) divided by the half-life. Alternatively, it can be calculated from measured decay data using lambda = -ln(N(t)/N0) / t.
Last reviewed: December 2025
Worked Examples
Example 1: Carbon-14 Decay Constant
Example 2: Finding Decay Constant from Measurement
Background & Theory
The Decay Constant Calculator applies the following established principles and formulas. Chemistry is the science of matter's composition, structure, properties, and transformations. At the heart of quantitative chemistry lies the mole concept. One mole of any substance contains exactly 6.022×10²³ entities (Avogadro's number, Nₐ), and the molar mass of an element or compound in grams per mole is numerically equal to its atomic or molecular mass in atomic mass units. This allows chemists to convert between measurable mass and the number of reacting particles. Stoichiometry uses balanced chemical equations to relate the amounts of reactants and products. A balanced equation conserves both mass and charge. Molarity, the most common concentration unit, is defined as M = n/V, where n is moles of solute and V is volume of solution in liters, giving units of mol/L. Acidity and basicity are quantified by the pH scale, defined as pH = −log₁₀[H⁺], where [H⁺] is the molar concentration of hydrogen ions. Pure water at 25°C has pH 7.00; acids have lower values and bases higher values. Each unit change represents a tenfold change in hydrogen ion concentration. Gas behavior is described by the ideal gas law PV = nRT, where P is pressure in pascals, V is volume in cubic meters, n is moles, R = 8.314 J/(mol·K), and T is temperature in kelvin. Special cases include Boyle's Law (P₁V₁ = P₂V₂ at constant temperature) and Charles's Law (V₁/T₁ = V₂/T₂ at constant pressure). Thermochemistry quantifies heat changes in reactions through enthalpy, H. Hess's Law states that the total enthalpy change for a reaction is the sum of enthalpy changes for any sequence of steps leading to the same overall reaction, making it possible to calculate enthalpies for reactions that cannot be measured directly. Electron configuration describes the distribution of electrons in atomic orbitals according to the Aufbau principle, Pauli exclusion principle, and Hund's rule. Periodic trends including atomic radius, ionization energy, and electronegativity arise systematically from electron configuration and nuclear charge, enabling chemists to predict and rationalize chemical behavior across the periodic table.
History
The history behind the Decay Constant Calculator traces back through the following developments. Chemistry's roots lie in alchemy, the medieval practice combining proto-scientific experimentation with mystical aims. Alchemists developed practical techniques including distillation, calcination, and the preparation of acids, building a body of empirical knowledge despite their theoretical misunderstandings. Modern chemistry is conventionally dated to Antoine Lavoisier (1743–1794), often called the father of modern chemistry. Lavoisier demonstrated the law of conservation of mass in 1789, showing that matter is neither created nor destroyed in chemical reactions. He identified oxygen's role in combustion, dismantling the phlogiston theory, and co-authored the first systematic chemical nomenclature, establishing the language still used today. John Dalton proposed the first modern atomic theory in 1803, asserting that all matter is composed of indivisible atoms, that atoms of the same element are identical in mass, and that compounds form from fixed ratios of different atoms. This provided a physical basis for Lavoisier's conservation law and Proust's law of definite proportions. Dmitri Mendeleev published his periodic table in 1869, arranging the 63 known elements by atomic mass and revealing repeating patterns of chemical behavior. He boldly left gaps for undiscovered elements and predicted their properties with remarkable accuracy, predictions confirmed by the subsequent discovery of gallium, scandium, and germanium. Ernest Rutherford's gold foil experiment in 1911 revealed the nuclear model of the atom: a tiny, dense, positively charged nucleus surrounded by electrons. Niels Bohr refined this in 1913 with a quantized model of electron orbits that explained the hydrogen emission spectrum. Quantum chemistry and molecular orbital theory, developed through the 1920s and 1930s, provided the full quantum mechanical description of chemical bonding. The latter 20th century saw the rise of computational chemistry, enabling molecular simulation at unprecedented scale. The green chemistry movement, articulated in the 12 Principles of Green Chemistry in 1998, reoriented the field toward sustainability, waste reduction, and benign chemical design, reflecting chemistry's growing awareness of its environmental responsibilities.
Frequently Asked Questions
Sources & References
Formula
lambda = ln(2) / t(1/2)
The decay constant equals the natural logarithm of 2 (0.693147) divided by the half-life. Alternatively, it can be calculated from measured decay data using lambda = -ln(N(t)/N0) / t.
Frequently Asked Questions
What is the decay constant?
The decay constant (lambda) is a probability rate that describes how quickly a radioactive substance undergoes nuclear decay. It represents the fraction of atoms that decay per unit time. A larger decay constant means faster decay and a shorter half-life. The relationship between decay constant and half-life is lambda = ln(2) / t(1/2), where ln(2) is approximately 0.693. The decay constant is an intrinsic property of each radioactive isotope and cannot be changed by chemical or physical means.
What is the relationship between decay constant and half-life?
The decay constant and half-life are inversely proportional: lambda = ln(2) / t(1/2). The half-life is the time required for half of a radioactive sample to decay. If the half-life is short, the decay constant is large and the substance decays rapidly. For example, Carbon-14 has a half-life of 5,730 years giving a decay constant of 1.21 x 10^-4 per year, while Polonium-214 has a half-life of only 164 microseconds with a much larger decay constant.
How is the decay constant used in radioactive dating?
In radioactive dating, the decay constant allows scientists to calculate the age of materials. By measuring the ratio of remaining parent isotope to daughter isotope, and knowing the decay constant, the age can be determined using t = -ln(N/N0) / lambda. Carbon-14 dating uses the known decay constant of C-14 to date organic materials up to about 50,000 years old. Uranium-lead dating uses the decay constants of U-238 and U-235 to date rocks billions of years old.
Is my data stored or sent to a server?
No. All calculations run entirely in your browser using JavaScript. No data you enter is ever transmitted to any server or stored anywhere. Your inputs remain completely private.
What inputs do I need to use Decay Constant Calculator accurately?
Each field is labelled with the required unit (metric or imperial). Gather your source values before starting — for example, a weight measurement in kilograms, a distance in metres, or a dollar amount — and enter them exactly as measured. The formula section on this page lists every variable and explains what each represents.
Can I use the results for professional or academic purposes?
You may use the results for reference and educational purposes. For professional reports, academic papers, or critical decisions, we recommend verifying outputs against peer-reviewed sources or consulting a qualified expert in the relevant field.
References
Reviewed by Manoj Kumar, Mathematics Educator · Editorial policy