Calculator
Formula used
Protein degradation is often modeled as first‑order decay: A(t) = A₀ · e^(−k t). Here, A₀ is the initial amount, A(t) is the remaining amount, k is the degradation rate constant, and t is time.
- t½ = ln(2) / k
- k = ln(A₀ / A) / t (two‑point estimate)
- k = −ln(p/100) / t (from percent remaining p)
Tip: If your data is not close to first‑order behavior, the half‑life becomes condition‑dependent.
How to use this calculator
- Pick a calculation mode that matches your available measurements.
- Enter values with consistent units (amount and time).
- Press Compute to view half-life directly under the header.
- Enable extra outputs to predict remaining percentage or time to a target level.
- Use the download buttons to export your most recent result.
Example data table
These examples assume first‑order decay and demonstrate typical outputs.
| # | A₀ (mg) | A (mg) | t (h) | k (1/h) | Half-life (h) |
|---|---|---|---|---|---|
| 1 | 100 | 50 | 6 | 0.1155 | 6.00 |
| 2 | 80 | 20 | 4 | 0.3466 | 2.00 |
| 3 | 120 | 30 | 8 | 0.1733 | 4.00 |
| 4 | 60 | 15 | 3 | 0.4621 | 1.50 |
| 5 | 200 | 100 | 12 | 0.0578 | 12.00 |
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Professional guide to protein half-life calculations
1) What “protein half-life” means in kinetics
In first-order degradation, half-life is the time required for the remaining protein amount to drop to 50% of its current value. This metric is widely used because it converts a rate process into an intuitive time scale. In cellular systems, reported half-lives commonly span minutes to days, depending on regulation and compartment.
2) The exponential decay model behind the calculator
This calculator assumes A(t)=A₀·e^(−kt), where k is constant across the measured interval. Under this model, decay is proportional to the amount present, producing a straight line when you plot ln(A) versus time. When your experiment matches this behavior, half-life becomes a stable summary parameter.
3) Key constants and quick reference data
The conversion from k to half-life is purely mathematical: t½ = ln(2)/k. The natural-log constant is ln(2) ≈ 0.6931. Time conversions used here are: 1 minute = 60 seconds, 1 hour = 3600 seconds, and 1 day = 86400 seconds.
4) Interpreting the rate constant in practical terms
Larger k means faster clearance and a shorter half-life. For example, if k = 0.10 1/h, then t½ ≈ 0.693/0.10 = 6.93 h. Doubling k halves the half-life, which helps compare conditions such as temperature, inhibitors, or mutations.
5) Two-point estimates from A₀, A, and time
When you have an initial amount A₀ and a later amount A after time t, the calculator computes k = ln(A₀/A)/t. Two-point estimates are convenient for pilot work, but they are sensitive to measurement noise. Whenever possible, confirm with multiple time points and replicate runs.
6) Using percent-remaining measurements
Some assays report remaining protein as a percentage instead of an absolute quantity. If p is the percent remaining at time t, the calculator uses k = −ln(p/100)/t. This approach is unit-robust because percent cancels the absolute scale, but it still assumes a constant k.
7) Forecasting remaining protein and time-to-target
Once k is estimated, you can predict how much remains after a future time: Remaining% = 100·e^(−kt). The calculator also computes the time to reach a target remaining fraction, useful for planning sampling windows. Example: reaching 10% remaining occurs at t = ln(10)/k.
8) Reporting, validation, and export-ready documentation
For professional reporting, record the calculation mode, units, and experimental context (cell line, temperature, treatment). Verify that A decreases monotonically and avoid using data where A ≥ A₀. The built-in CSV and PDF exports capture the latest run for sharing, archiving, and lab notebook traceability.
FAQs
1) What model does this calculator assume?
It assumes first-order exponential decay: the degradation rate is proportional to the current amount. If your system deviates (e.g., saturation or bursts), interpret results as an approximation over the measured interval.
2) Why must A be smaller than A₀ in two-point mode?
Because the formula uses ln(A₀/A). If A is not smaller, the decay estimate becomes zero or negative, which contradicts a degradation process and indicates inconsistent inputs or growth.
3) Which units should I use for time?
Use the unit that matches your experiment (seconds, minutes, hours, or days). The calculator converts to seconds internally for accuracy, then displays half-life in your selected unit.
4) Can I compute half-life directly from k?
Yes. Choose the “rate constant” mode, enter k with its unit (1/s, 1/min, 1/h, or 1/day), and the tool calculates t½ = ln(2)/k automatically.
5) What if my assay reports percent remaining?
Select the percent mode and enter the percent remaining and elapsed time. The calculator uses k = −ln(p/100)/t, then converts k into half-life.
6) How accurate is a two-point half-life?
Two-point estimates are useful for quick checks but can be sensitive to measurement noise. For better precision, collect multiple time points, fit ln(A) versus time, and compare the fitted k.
7) What do the download buttons export?
They export the most recent calculation stored in this session. CSV is convenient for spreadsheets, and the PDF is a lightweight report summarizing inputs, k, half-life, and optional predictions.