Prediction Probability Tool Calculator

Calculator

Pick a method, enter inputs, and compute a probability.

Method

Choose how your probability should be computed.

Display

Controls how probability-like values are shown.

Decimals

Use fewer decimals for cleaner reports.

Threshold

Used to label the result Positive/Negative.

Logistic input

Use z if you already have a model score.

Metrics scale

Applies to sensitivity, specificity, prevalence inputs.

Predicted label

Computes PPV (positive) or NPV (negative).

Odds type

Pick whether you have odds or log-odds.

Odds / log-odds value

Odds must be ≥ 0. Log-odds can be any value.

Logistic inputs

Linear score z

p = 1 / (1 + e^−z).

Intercept b0

Start with an intercept, then add bᵢxᵢ terms.

Feature x1

Coefficient b1

Leave unused pairs blank.

Feature x2

Coefficient b2

Feature x3

Coefficient b3

Feature x4

Coefficient b4

Feature x5

Coefficient b5

Linear score: z = b0 + Σ(bᵢxᵢ). Then probability p = 1/(1+e^−z).

Metrics inputs

Sensitivity

True positive rate (TP/(TP+FN)).

Specificity

True negative rate (TN/(TN+FP)).

Prevalence

Prior probability of the event in your population.

Optional: enter counts to derive metrics

TP

FP

TN

FN

If all four counts are provided, sensitivity/specificity/prevalence are derived automatically.

Example data table

Use these sample values to validate your setup.

Scenario	Inputs	Output
Logistic (coefficients)	b0 = -1.5, x1 = 2.0, b1 = 0.8, x2 = 1.0, b2 = 0.6	z = 0.7 → p ≈ 0.6682
Metrics (PPV)	Sensitivity = 91%, Specificity = 88%, Prevalence = 12%, Predicted = Positive	PPV ≈ 0.5084
Odds conversion	Odds = 3.0	p = 3/(1+3) = 0.75

Formula used

1) Logistic probability

z = b0 + Σ(bᵢxᵢ)

p = 1 / (1 + e^−z)

This is common for logistic regression and calibrated linear model scores.

2) Odds conversion

Odds = p / (1 − p)

p = Odds / (1 + Odds)

Useful when your model outputs odds rather than probabilities.

3) Metrics-based probability (Bayes)

PPV = (Se·Prev) / (Se·Prev + (1−Sp)·(1−Prev))

NPV = (Sp·(1−Prev)) / (Sp·(1−Prev) + (1−Se)·Prev)

Se = sensitivity, Sp = specificity, Prev = prevalence in the target population.

How to use this calculator

Select a computation method that matches your data source.
Enter inputs; use percent or decimal formats where indicated.
Set a threshold if you want Positive/Negative labeling.
Click Calculate Probability to see results above the form.
Use Download CSV or Download PDF to export the current run.
Review your session history to compare multiple runs.

Interpreting probability outputs for decisions

A predicted probability is a calibrated estimate of event likelihood for similar cases. For example, p=0.72 suggests about 72 events per 100 comparable records, assuming stable data and correct calibration. Use percent or decimal display to match stakeholders, and keep rounding consistent when comparing runs. Use the threshold control to translate probability into a Positive or Negative label, but retain the numeric probability for ranking and prioritization.

Choosing an input pathway that matches your model

If your workflow produces a linear score z, apply the sigmoid p=1/(1+e^−z) to map any real value into 0–1. A useful anchor is z=0, which always returns p=0.50. If you store coefficients, compute z=b0+Σ(bᵢxᵢ) using up to five feature pairs. If you receive odds from a scoring engine, convert with p=odds/(1+odds) to preserve interpretability.

Using sensitivity, specificity, and prevalence with Bayes

Operational performance depends on base rates. With sensitivity 0.91, specificity 0.88, and prevalence 0.12, the positive predictive value is about 0.51, meaning roughly half of positive flags are true events. Likelihood ratios summarize evidence: LR+=Se/(1−Sp) and LR−=(1−Se)/Sp, updating prior odds into posterior odds. Switching to a negative prediction yields NPV near 0.99 in the same setting, which is useful for ruling out cases efficiently.

Selecting thresholds with cost and capacity constraints

A 0.50 threshold is conventional, not optimal. When false positives are expensive, raise the threshold to improve precision at the expense of recall. When missing events is costly, lower the threshold and allocate capacity downstream. Sweep thresholds and record TP, FP, TN, and FN to compare operating points objectively. Track expected counts per 10,000 to translate abstract rates into staffing, review time, and budget impact.

Creating audit-ready outputs for teams and reports

Consistent reporting reduces rework. Export CSV to share values with analysts and build dashboards, and export PDF for static reviews and approvals. Use the session history to compare runs across thresholds, input styles, and population assumptions, then document the chosen method, parameters, and timestamp for reproducibility.

FAQs

1) What does the probability represent?

It estimates the chance of the selected outcome for similar future cases, given the inputs and assumptions. It is not a guarantee, and it depends on calibration and how closely new data matches training data.

2) When should I use the Metrics method?

Use it when you know sensitivity, specificity, and prevalence, or you have TP/FP/TN/FN counts. It converts those rates into PPV or NPV, which directly answers how often a positive or negative prediction is correct.

3) Why can PPV be low with strong sensitivity?

If prevalence is small, false positives can outnumber true positives even when sensitivity is high. PPV rises when prevalence increases, specificity improves, or you raise the decision threshold to reduce false positives.

4) How do I choose a threshold?

Start with your business cost trade‑off: raise the threshold to reduce false alarms, lower it to catch more events. Then validate using a holdout set and review expected TP/FP counts per 10,000 for capacity planning.

5) What is the difference between odds and probability?

Probability ranges from 0 to 1. Odds compare event to non‑event likelihood: odds = p/(1−p). Converting back uses p = odds/(1+odds), which the tool computes automatically.

6) Can I use this for multiclass predictions?

This calculator is designed for binary outcomes. For multiclass models, compute a one‑vs‑rest probability for the class you care about, or use the model’s softmax probabilities and interpret each class separately.