# Exponential Growth & Decay Calculator

Calculate exponential growth or decay with doubling/halving time, final values, and period-by-period projections.

## What this calculates

Model exponential growth or decay processes. Enter an initial value, growth or decay rate, and number of periods to find the final value, doubling or halving time, and period-by-period progression.

## Inputs

- **Initial Value** — min 0 — Starting value (population, investment, quantity, etc.).
- **Growth Rate (% per period)** — min -99.99, max 1000 — Percentage change per period. Positive for growth, negative for decay.
- **Number of Periods** — min 1, max 100 — Number of time periods (years, months, etc.).
- **Mode** — options: Growth, Decay — Growth increases over time; decay decreases. Decay uses the absolute value of the rate.

## Outputs

- **Final Value** — Value after the specified number of periods.
- **Total Change** — Absolute change from initial to final value.
- **Doubling/Halving Time** — Number of periods to double (growth) or halve (decay).
- **Values (first 5 periods)** — formatted as text — Value at each of the first 5 periods.
- **Total % Change** — Overall percentage change from initial to final.

## Details

Exponential growth and decay describe processes where the rate of change is proportional to the current value. The formula is A = P x (1 + r)^t, where P is the initial value, r is the rate per period, and t is the number of periods.

Doubling and halving time: For growth, the doubling time is ln(2) / ln(1 + r). For decay, the halving time (half-life) uses the same formula with ln(0.5). At 7% growth, the doubling time is about 10.24 periods, close to the Rule of 72 estimate (72/7 = 10.3).

Applications: Exponential models appear throughout science and finance: population growth, compound interest, radioactive decay, bacterial cultures, viral spread, depreciation, and drug metabolism. Real-world growth is often exponential only for limited periods before other factors (resource limits, competition) cause it to slow.

## Frequently Asked Questions

**Q: What is the Rule of 72?**

A: The Rule of 72 is a quick approximation: doubling time equals 72 divided by the growth rate percentage. For 6% growth, doubling takes approximately 72/6 = 12 periods. It is most accurate for rates between 2% and 10%. The exact formula is ln(2)/ln(1+r).

**Q: What is the difference between exponential and linear growth?**

A: Linear growth adds a constant amount each period (e.g., +100 per year). Exponential growth adds a constant percentage (e.g., +5% per year), meaning the absolute amount increases over time. Exponential growth starts slow but eventually far outpaces linear growth.

**Q: When does exponential growth stop in the real world?**

A: Real exponential growth is limited by resources, space, or other constraints. Populations follow logistic growth (S-curve) as carrying capacity is approached. Investments face market limits. True unbounded exponential growth is a mathematical idealization.

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Source: https://vastcalc.com/calculators/math/exponential-growth
Category: Math
Last updated: 2026-04-21