Exponential Growth Prediction Calculator

Project a future value from steady exponential growth. Enter a starting value, a growth rate per period, and the number of periods to get the predicted amount, total growth, and doubling time using A = P(1 + r)t.

Quick Facts

Formula
A = P(1 + r)t
Discrete exponential growth. Rate r is entered as a percent and used as a decimal; each period multiplies the value by (1 + r).

Your Results

Calculated
Predicted value
-
A = P(1 + r)^t
Total growth
-
Increase over the starting value
Growth multiple
-
Final ÷ starting value
Doubling time
-
Periods to double at this rate

Ready

Enter a starting value, growth rate, and number of periods, then calculate.

Understanding exponential growth prediction

Exponential growth happens when a quantity increases by a constant percentage each period rather than by a constant amount. Because each period's growth is applied to a larger base than the one before, the total accelerates over time. This calculator predicts the future value of such a quantity from three inputs: the starting value, the growth rate per period, and the number of periods.

The formula

The discrete exponential growth model is:

A = P(1 + r)t

  • A = predicted (future) value
  • P = starting value, P₀
  • r = growth rate per period as a decimal (enter 5 for 5%, which the tool converts to 0.05)
  • t = number of periods

Each period multiplies the running total by the factor (1 + r). Growing $1,000 at 5% per year for 10 years gives 1000 × 1.0510 ≈ $1,628.89. A negative rate models exponential decay: entering −10% shrinks the value by a factor of 0.9 each period.

Discrete vs. continuous growth

The formula above compounds once per period. When growth is truly continuous — compounded every instant — the model becomes A = P·ert, where e ≈ 2.71828. Continuous compounding always yields a slightly larger result for the same nominal rate: at r = 5% for one year, (1.05) = 1.05 versus e0.05 ≈ 1.05127. This calculator uses the discrete form, which matches how most real-world rates (annual interest, yearly population figures, per-round metrics) are quoted.

Doubling time and the Rule of 72

A hallmark of exponential growth is a fixed doubling time that does not depend on the starting value. The exact doubling time is t = ln(2) / ln(1 + r). The Rule of 72 is a fast mental estimate: divide 72 by the percent rate. At 6% per period the rule gives 72 ÷ 6 = 12 periods, while the exact value is ln(2)/ln(1.06) ≈ 11.90 periods — close enough for quick checks.

Common reference points

  • 7% ≈ doubles in ~10 periods (ln 2 / ln 1.07 ≈ 10.24). A long-run stock-market rule of thumb.
  • 2% ≈ doubles in ~35 periods (≈ 35.0). Typical of slow population or inflation growth.
  • 100% growth rate means the quantity doubles every single period (multiplier 2).
  • Bacterial growth is a classic case: a colony dividing every 20 minutes has r = 100% per 20-minute period.

Frequently Asked Questions

What formula does this exponential growth calculator use?
It uses the discrete exponential growth formula A = P(1 + r)t, where P is the starting value, r is the growth rate per period as a decimal, and t is the number of periods. For example, 1,000 growing at 5% per year for 10 years gives 1000 × 1.0510 ≈ 1,628.89.
Can I model decay instead of growth?
Yes. Enter a negative growth rate. For example, −10% per period multiplies the value by 0.9 each period, so 1,000 becomes 1000 × 0.95 ≈ 590.49 after 5 periods. The calculator reports how many periods it takes the value to halve. This is an important design consideration because small changes in this variable can have a disproportionate effect on the final result. The calculator models multiple inputs simultaneously so you can adjust this parameter and immediately see how it shifts the outcome. Where possible, use measured or verified values rather than default estimates for the most reliable output.
How do I find the doubling time?
The exact doubling time is t = ln(2) / ln(1 + r). A quick estimate is the Rule of 72: divide 72 by the percent growth rate. At 6% per period, 72 ÷ 6 = 12 periods, while the exact value is ln(2)/ln(1.06) ≈ 11.90 periods.
Can I model decay instead of growth?
Yes. Enter a negative growth rate. For example, −10% per period multiplies the value by 0.9 each period, so 1,000 becomes 1000 × 0.95 ≈ 590.49 after 5 periods. The calculator reports how many periods it takes the value to halve.
Does the period have to be years?
No. A period can be any consistent time step — years, months, days, or event rounds — as long as the growth rate is expressed per that same period. Just make sure t and r use the same unit. To convert an annual rate to a monthly one, use (1 + annual)1/12 − 1 rather than dividing by 12.

Common Tip Percentages

ServiceTypical Tip RangeNotes
Restaurant (sit-down)15–20%20%+ for exceptional service
Food delivery10–20%Consider extra for long distances
Taxi / rideshare10–20%More for assistance with luggage
Hotel housekeeping$2–5/nightLeave daily, not just at checkout
Barber / hair salon15–20%On pre-discount total
Pizza delivery10–15% or $3–5 minimumHigher in bad weather

General Household Budget Ratios (50/30/20 Rule)

Category% of Net IncomeExamples
Needs50%Rent, groceries, utilities, insurance
Wants30%Dining out, entertainment, hobbies
Savings / Debt20%Emergency fund, retirement, extra payments

Common Measurement Conversions for Everyday Use

QuantityUS / ImperialMetric Equivalent
1 cup8 fl oz237 mL
1 pint16 fl oz473 mL
1 quart32 fl oz946 mL
1 gallon128 fl oz3.785 L
1 lb16 oz453.6 g
1 ft12 in30.48 cm

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