Calculator Inputs
Example Data Table
| Case | Radius cm | Distance cm | Activity Bq | Yield | Time s | Use Case |
|---|---|---|---|---|---|---|
| Small lab source | 2 | 10 | 500000 | 0.85 | 60 | Bench check |
| Wide disk source | 8 | 15 | 2500000 | 1 | 120 | Area exposure |
| Shielding review | 5 | 30 | 1000000 | 0.5 | 300 | Distance study |
Formula Used
The calculator treats the disk as a uniform circular source. Each small ring emits isotropically. The axial fluence rate is found by integrating inverse square contribution over the disk area.
Source area:
A = πR²
Total particle emission rate:
Q = Activity × Emission Yield
Surface emission rate:
q = Q / A
Numerical attenuated fluence rate:
φ = (q / 2) × ∫[0 to R] ρ exp(-μ√(ρ²+z²)) / (ρ²+z²) dρ × B
Total fluence:
Φ = φ × t
Dose estimate:
D = Φ × Dose Coefficient
The non-attenuated closed form is:
φ = (q / 4) × ln(1 + R² / z²)
The on-axis solid angle of the circular disk is:
Ω = 2π(1 - z / √(z² + R²))
How to Use This Calculator
- Enter the active disk radius in centimeters.
- Enter the axial distance from the disk center to the point of interest.
- Add source activity in becquerels and emission yield per decay.
- Set exposure time, attenuation coefficient, and buildup factor.
- Enter detector area if you want estimated particle count.
- Add a fluence-to-dose coefficient for dose estimation.
- Press the calculate button to show results above the form.
- Use CSV or PDF download buttons to save the report.
Radiation Disk Source Fluence Guide
What This Tool Measures
Disk source fluence is useful when a radioactive surface is not point shaped. A circular source can expose a detector from many small surface elements. Each element has a different path length. The center line is the easiest geometry to model. This calculator focuses on that axial case.
Why Disk Geometry Matters
A point source model may overstate or understate exposure near a broad disk. The error becomes larger when the distance is similar to the source radius. A disk integral gives a better estimate. It includes source size, distance, activity, yield, and exposure time. It also includes optional attenuation.
Attenuation and Buildup
Attenuation reduces particle fluence along each slant path. The coefficient should match the material and radiation energy. Buildup can raise the result when scattered radiation contributes. Use a value of one when no buildup correction is needed. Use measured or referenced data for critical studies.
Dose and Detector Estimates
Fluence is not the same as absorbed dose. A dose coefficient converts fluence into an estimated dose quantity. This coefficient depends on radiation type, energy, and target material. Detector particle count is found by multiplying fluence by detector area. It is an ideal estimate. Real detector efficiency may be lower.
Good Practice
Keep units consistent. Use centimeters for length inputs. Check activity and emission yield carefully. Choose attenuation data from a trusted source. Add uncertainty when measurements or coefficients are approximate. Review results with radiation safety rules before using them in real work. This tool supports planning, education, and first-pass shielding checks.
Frequently Asked Questions
1. What is disk source fluence?
It is the number of emitted particles crossing each square centimeter at a point near a circular radiation source.
2. Is this a point source calculator?
No. It integrates contribution across a circular disk, so source radius affects the final fluence estimate.
3. What does axial distance mean?
It is the straight distance from the disk center to the calculation point along the disk centerline.
4. What should I enter for emission yield?
Enter particles emitted per decay. Use one for one particle per decay, or use a branching fraction when applicable.
5. What is the buildup factor?
It is a multiplier for scattered radiation contribution. Use one when scattered contribution is ignored.
6. Why is attenuation coefficient needed?
It estimates loss through air, shielding, or another medium. The value must match radiation energy and material.
7. Can this estimate dose?
Yes. Enter a fluence-to-dose coefficient. The result is only as accurate as the coefficient and input data.
8. Is this enough for official safety approval?
No. Use it for planning and checks. Formal radiation work needs qualified review and approved safety methods.