F18 Half Life Calculator: Decay & Dose

This calculator works out the remaining activity of Fluorine-18 (F-18) after a given decay time, and also tells you how much has decayed away. You enter the starting activity (in MBq or mCi), the elapsed time, and the calculator returns the current activity and the fraction remaining, using the standard physical half-life of 109.77 minutes.

Formula

The decay of any radioactive isotope follows the exponential decay law. For F-18, the formula is:

A(t) = A₀ × e^−λt

where:

• A(t) = activity remaining after time t (MBq or mCi)
• Aâ‚€ = initial activity (MBq or mCi)
• λ = decay constant = ln(2) / T_1/2 = 0.693 / 109.77 min ≈ 0.006314 min^−1
• t = elapsed time (minutes)
• T_1/2 = half-life = 109.77 minutes (about 1.83 hours)

The fraction remaining is simply e^−λt, and the decayed amount is A₀ minus A(t). The calculator uses minutes for time because that is the standard unit in nuclear medicine workflows.

Worked Example

Using the default values: initial activity 370 MBq, decay time 60 minutes.

1. Compute λ: 0.693 / 109.77 = 0.006314 min^−1
2. Multiply by time: 0.006314 × 60 = 0.37884
3. Take e^{−0.37884} ≈ 0.6846
4. Remaining activity: 370 × 0.6846 = 253.3 MBq
5. Fraction remaining: 68.46%
6. Decayed: 370 − 253.3 = 116.7 MBq

The calculator shows 253.30 MBq remaining, 68.46% fraction, and 116.70 MBq decayed, matching these steps.

Why F-18 Half-Life Matters

Fluorine-18 is the most common radioisotope used in PET (Positron Emission Tomography) imaging. It is produced in a cyclotron and then attached to a molecule like FDG (fluorodeoxyglucose) to trace metabolic activity. Because its half-life is only 109.77 minutes, the activity drops by half every 1.83 hours. This short half-life is both an advantage and a challenge:

• Advantage: Patient radiation dose is low, and the isotope clears from the body quickly.
• Challenge: The tracer must be produced, transported, and injected within a few hours. A dose that leaves the cyclotron at 10:00 AM will have only about 25% of its original activity by 4:00 PM.

In practice, radiopharmacists calculate the required initial activity so that the patient receives the prescribed dose at injection time. That calculation is exactly what this calculator does in reverse.

How to Use the Calculator for Real Work

Enter the activity you have now and the time until you need to use it. The calculator tells you what will be left. For example:

• A vial contains 1,500 MBq at 8:00 AM. You plan to inject at 10:30 AM (150 minutes later). Enter 150 minutes – the result shows 1500 × e^{−0.006314×150} = 1500 × 0.387 ≈ 580 MBq.
• To find out how much activity you need to order so that 370 MBq remains after 90 minutes, you would divide 370 by e^{−0.006314×90} = 370 / 0.566 ≈ 654 MBq.

Always use the same unit for input and output. If you enter MBq, the result is MBq; if you enter mCi, the result is mCi. Do not mix units in one calculation.

Common Mistakes and Misconceptions

One frequent error is using the decay constant in hours instead of minutes, or vice versa. The half-life is 109.77 minutes, so if you enter time in hours, you must convert to minutes first (multiply by 60). Another common mistake is using the biological half-life instead of the physical half-life. F-18 has a physical half-life of 109.77 minutes, but its biological half-life in the body is different (about 16 hours for FDG). The calculator uses the physical half-life because that governs radioactive decay regardless of biological clearance.

Some people also confuse “remaining activity� with “decayed activity.� The sum of the two always equals the initial activity. If you have 100 MBq and 30% remains, then 70% has decayed.

Rounding too early can cause small errors. Keep at least 4 significant figures in intermediate steps, as the calculator does.

Limits of the Formula

The exponential decay law is exact for a pure sample of F-18 with no impurities. In practice, cyclotron-produced F-18 may contain trace impurities, but they are usually negligible for clinical use. The formula does not account for:

• Chemical or biological processes (e.g., metabolism of FDG)
• Physical losses (e.g., spillage, adsorption to container walls)
• Variations in half-life due to environmental conditions – these are so small they are unmeasurable for practical purposes

For dose calibration, always use a dose calibrator to measure actual activity, not just the calculated value. The calculator is a planning tool, not a substitute for measurement.

Comparing F-18 to Other PET Isotopes

F-18 is one of several positron emitters used in PET. Its half-life is longer than some, shorter than others:

• Carbon-11: 20.4 minutes – requires on-site cyclotron, used for neuroreceptor studies.
• Nitrogen-13: 9.97 minutes – used for myocardial perfusion.
• Oxygen-15: 2.04 minutes – used for blood flow studies.
• Gallium-68: 67.7 minutes – generator-produced, used for somatostatin receptor imaging.
• Rubidium-82: 1.27 minutes – generator-produced, used for cardiac PET.

F-18’s 109.77-minute half-life is a sweet spot: long enough to allow transport from a regional cyclotron, but short enough to keep patient doses low. That is why it dominates clinical PET.

Safety and Handling Considerations

F-18 emits positrons, which annihilate with electrons to produce two 511 keV gamma rays. This requires shielding and careful handling. Key points:

• Use lead or tungsten shielding for syringes and vials.
• Minimize exposure time and maximize distance from the source.
• Wear dosimeters and follow local radiation safety regulations.
• After injection, patients are a source of radiation for a few hours; they should avoid close contact with pregnant women and young children for the rest of the day.

The short half-life means that after 10 half-lives (about 18.3 hours), less than 0.1% of the original activity remains, so waste decays quickly. However, always follow institutional rules for radioactive waste disposal.

Frequently Asked Questions

What is the half-life of F-18 in minutes and hours?

The physical half-life is 109.77 minutes, which is 1 hour 49.8 minutes, or about 1.83 hours. This is the time for half of the radioactive atoms to decay.

How do I convert mCi to MBq for this calculator?

1 mCi = 37 MBq. So if you have 10 mCi, that is 370 MBq. The calculator accepts either unit, but you must use the same unit for input and output.

Why does F-18 decay so fast compared to other medical isotopes?

F-18 is a positron emitter with a relatively short half-life by design. It allows PET imaging with a low radiation dose to the patient. Other isotopes like Technetium-99m (6 hours) are used for SPECT, not PET, and have different decay properties.

Can I use this calculator for FDG specifically?

Yes, because the radioactive part is F-18. FDG is just F-18 attached to a glucose molecule. The physical decay is identical. However, biological clearance is not included; the calculator only handles radioactive decay.

What is the difference between physical and biological half-life?

Physical half-life is the time for half the atoms to decay (109.77 min for F-18). Biological half-life is the time for half the substance to be removed from the body by biological processes (about 16 hours for FDG). The effective half-life combines both and is shorter than either alone.

How much activity remains after 6 hours (360 minutes)?

Using the formula: fraction = e^{−0.006314×360} = e^−2.273 ≈ 0.103, so about 10.3% remains. If you started with 1000 MBq, you would have about 103 MBq left.

Related

• EE Score Calculator: How to Estimate Your Energy Performance
• Echo LV Mass Calculator: Formula & Use
• ECU GPA Calculator: How to Compute Your Grades

in act | Initial activity | MBq | 370 | 0
in t | Decay time | min | 60 | 0
out rem | Remaining activity | MBq | act * exp(-ln(2) * t / 109.77) | 2
out frac | Fraction remaining | % | 100 * exp(-ln(2) * t / 109.77) | 2
out decayed | Decayed activity | MBq | act - act * exp(-ln(2) * t / 109.77) | 2