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Exponential Decay Calculator

Solve P(t) = P₀·e^(−rt) for any variable, with the half-life.

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Open Exponential Decay Calculator and you get an answer straight away, with no account to create. You will find it under Algebra & equations, with Exponential Equation Solver and Exponential Growth Calculator for the neighbouring cases.

How to use it

  1. Open the tool — no signup or install needed.
  2. Enter your input or adjust the available options.
  3. Get your result instantly, then copy or download it.

Frequently asked questions

What does Exponential Decay Calculator do?

Solve P(t) = P₀·e^(−rt) for any variable, with the half-life.

When would I actually use this?

Getting through a problem set: solving for the unknown, factoring an expression, and — more usefully — seeing the steps that got there.

What is the most common mistake?

Losing a solution when both sides are squared or divided by an expression. Squaring can add roots that do not satisfy the original equation, and dividing can remove one — check every answer back in the original.

How is Exponential Decay Calculator different from Exponential Equation Solver?

They sit next to each other but answer different questions: Exponential Equation Solver is the one to open when you need it to solve exponential equations of six types — basic, coefficient, linear exponent, two bases, quadratic-in-a^x and shifted — with logarithms and a full step-by-step solution. Pick whichever matches what you're starting from — both are free.

Is there a tool for the next step?

Exponential Growth Calculator is the closest one after this: Solve P(t) = P₀·(1+r)^t for any variable, with the doubling time.

What else is worth having open alongside it?

Exponential Distribution Calculator and Exponential Integral Calculator — they come up in the same task often enough to be worth a second tab.

Where do the figures come from?

The algebra is symbolic where the expression allows it and numeric otherwise, and the tool says which it used. Exact results are given as fractions or radicals rather than rounded decimals.

Further reading

All guides →
ExplainerHow Half-Life Works: What Is Left After 1, 3 and 10 Half-LivesOne half-life leaves 50%, three leave 12.5%, ten leave less than a tenth of a percent. The formula is a single line — the part worth understanding is why the answer never reaches zero.How-toHow to Use the Quadratic Formula: Solving ax² + bx + c = 0Solve any quadratic equation with x = (−b ± √(b² − 4ac)) / 2a, and read the discriminant to know how many real solutions to expect.How-toHow to Find a Cube Root by HandA step-by-step guide to finding a cube root by estimation and refinement — plus how it differs from a square root and when a value stays irrational.ExplainerHow Exponents Work: Powers and the Laws of ExponentsAn exponent is repeated multiplication. Learn the laws of exponents, what negative and fractional powers mean, and why anything to the zero is one.ExplainerThe Flat Pattern of a Cone Is a Sector, Not a CircleRoll a 50 mm cone 80 mm tall and its pattern is a 190.8° slice of a 94 mm circle. Flatten a nearly cylindrical lampshade and the pattern radius runs to 839 mm — the shallower the taper, the further away the apex.ExplainerA 1 % Drop Rate Does Not Mean One Hundred RunsAt 1 %, a hundred attempts give you 63.4 % — not certainty. Ninety per cent takes 230 attempts and ninety-nine takes 459, and more than a third of players are still empty-handed at a hundred.