Exponential Decay Calculator High Precision

Calculate exponential decay using high precision calculations. This calculator can be used to model processes where the rate of decay is proportional to the current value, such as radioactive decay, population decline, or cooling of objects.

Input Parameters

Calculation Results

Calculation Formula

A = A₀ × e-λt

Where:
A = Final amount
A₀ = Initial amount
λ = Decay rate per time period
t = Time period
e = Euler's number (approximately 2.71828)

Result

Final Amount (A): -

Amount Remaining: - %

Time Elapsed: - periods

Exponential Decay Calculator High Precision Usage Guide

Learn how to use the Exponential Decay Calculator High Precision calculator and its working principles

How to Use This Calculator

  1. Enter your Initial Amount (A₀) - the starting value before decay begins.
  2. Input the Decay Rate (λ) as a decimal. For example, if something loses 5% of its value per time period, enter 0.05.
  3. Specify the Time Period (t) for which you want to calculate the decay.
  4. Click the Calculate button to see the results.
  5. The calculator will display the final amount, the percentage remaining, and confirm the time period used.

Understanding Exponential Decay

Exponential decay describes a process where the rate of decrease is proportional to the current value. The formula used is:

A = A₀ × e-λt

This formula appears in many natural processes:

  • Radioactive decay in physics
  • Population decline in biology
  • Cooling of objects in thermodynamics
  • Drug concentration in pharmacokinetics
  • Compound interest calculations (as decay)

Example

Suppose you have 100 grams of a radioactive substance with a decay rate of 0.1 per year. You want to know how much remains after 5 years:

  1. Initial Amount (A₀) = 100
  2. Decay Rate (λ) = 0.1
  3. Time Period (t) = 5
  4. Calculation: A = 100 × e-0.1 × 5 = 100 × e-0.5 ≈ 100 × 0.60653 = 60.653

After 5 years, approximately 60.65% of the original substance remains.