Use this calculator to model gradual health changes such as rehab minutes, dosage titration, water intake, calorie targets, or step goals.
Educational planning tool only. It does not replace professional medical advice, diagnosis, or treatment.
Calculator
Choose a health scenario, define the gradient pattern, and estimate period-by-period values with totals and present worth.
Example Data Table
Example: weekly walking rehab plan with an arithmetic gradient of 5 minutes per week.
| Week | Planned Minutes | Increase | Cumulative Minutes |
|---|---|---|---|
| 1 | 20 | 0 | 20 |
| 2 | 25 | 5 | 45 |
| 3 | 30 | 5 | 75 |
| 4 | 35 | 5 | 110 |
| 5 | 40 | 5 | 150 |
| 6 | 45 | 5 | 195 |
Formula Used
Arithmetic gradient series
Period value: At = A1 + (t - 1)G
Nominal total: S = n / 2 × [2A1 + (n - 1)G]
Meaning: each period changes by the same fixed amount.
Geometric gradient series
Period value: At = A1 × (1 + g)(t - 1)
Nominal total: S = A1 × [(1 + g)n - 1] / g, for g ≠ 0
Meaning: each period changes by the same percentage rate.
Present worth and equivalent uniform value
Present worth: P = Σ [At / (1 + i)t]
Equivalent uniform value: E = P × [i(1 + i)n] / [(1 + i)n - 1], when i ≠ 0
Air pressure gradient between locations A and B
Pressure gradient: (PA − PB) / distance, in millibars per kilometer.
A–a gradient
Definition: A–a gradient = PAO2 − PaO2
Alveolar oxygen estimate: PAO2 = FiO2(Patm − PH₂O) − PaCO2 / R
How to Use This Calculator
- Select the health scenario and the series type.
- Enter the starting value, number of periods, and unit label.
- For arithmetic mode, enter the fixed change per period.
- For geometric mode, enter the percentage change per period.
- Add an adjustment rate if you want present worth and equivalent uniform values.
- Optionally set lower and upper targets to flag values outside your preferred range.
- Click the calculate button to display the results block above the form.
- Use the CSV and PDF buttons to export the table and summary.
FAQs
1) What is a gradient series in health planning?
A gradient series models values that rise or fall over time. In health planning, it can represent weekly rehab minutes, gradual dosage changes, hydration targets, or progressive activity goals across future periods.
2) When should I use arithmetic instead of geometric mode?
Use arithmetic mode when the change is a fixed amount each period, like adding 5 minutes weekly. Use geometric mode when the change is percentage-based, like increasing a target by 10% each month.
3) What does present worth mean here?
Present worth discounts future values back to a common starting point. It helps compare a changing plan with an equivalent constant plan when you apply an adjustment or discount rate.
4) Can this calculator handle decreasing series?
Yes. Use a negative arithmetic gradient for fixed decreases or a negative percentage for shrinking geometric plans. This is useful for tapering targets, controlled step-down programs, or gradual reductions.
5) How do I calculate the air pressure gradient between locations A and B in millibars per kilometer?
Subtract the pressure at location B from location A, then divide by the distance in kilometers. Example: (1012 − 1000) ÷ 24 = 0.5 millibars per kilometer.
6) How to calculate A-a gradient?
Use A–a gradient = PAO₂ − PaO₂. Estimate PAO₂ from FiO₂(Patm − PH₂O) − PaCO₂/R, then subtract arterial oxygen. It helps assess oxygen transfer from alveoli to blood.
7) What do the lower and upper targets do?
They classify each period as below target, within range, or above target. This makes it easier to review whether a plan stays inside a preferred intensity or dosage window.
8) What gets exported in the CSV and PDF files?
The exports include the calculated summary and the period-by-period results table. The PDF also captures the visible results block, including the chart and the detailed values shown on screen.
© 2026 Gradient Series Calculator for Health Planning.