How to Find a Z-Score Using Excel Solver Step by Step

To find a z-score from a cumulative probability, put a starting z value in one cell, calculate its standard normal cumulative probability in another, then use Solver to make that probability equal your target. For example, with a starting z-score in B2, the calculation is =NORM.S.DIST(B2,TRUE). Solver adjusts B2 until the result matches your target probability. You will need desktop Excel and the Solver add-in.

What You’ll Need

Microsoft Excel for Microsoft 365 on Windows, or desktop Excel for Mac. Solver is not available to run in Excel for the web; open the workbook in the desktop app.
The probability you want to work backward from. Use a cumulative probability between 0 and 1, such as 0.95 for the 95th percentile.
The Solver add-in enabled. If it is not installed or turned on, the steps below explain how to enable it.
If you are solving for a raw score rather than a standard z-score, the distribution’s mean and standard deviation.

Step-by-Step

Decide what probability you mean. The standard normal cumulative probability is the area to the left of a z-score. A left-tail probability of 0.95 therefore corresponds to a positive z-score of about 1.645. A left-tail probability of 0.05 corresponds to about -1.645. If you have an upper-tail probability, convert it to a left-tail probability by subtracting it from 1. For example, an upper-tail area of 0.05 becomes a cumulative target of 0.95. For a two-sided 95% interval, the positive critical value uses a cumulative target of 0.975; the negative critical value is its opposite.
Set up three cells for a standard z-score. In A2, enter the cumulative target probability, such as 0.95. In B2, enter a starting guess for z, such as 0. In C2, calculate the cumulative probability for that guess. With the target in A2 and the starting z value in B2, enter this formula in C2: =NORM.S.DIST(B2,TRUE). For B2 equal to 0, C2 returns 0.5. The formula uses the standard normal distribution and TRUE requests the cumulative result rather than the density.
Enable Solver if needed. In Windows Excel, select File > Options > Add-ins. At the bottom, next to Manage, choose Excel Add-ins and select Go. Check Solver Add-in, then select OK. On Excel for Mac, use Tools > Excel Add-ins, select Solver Add-in, and confirm. After it is enabled, Solver appears on the Data tab in desktop Excel. Menu wording or placement can vary slightly by Excel release.
Open the Solver Parameters dialog. Select Data > Solver. Set the objective to C2, the cell containing the calculated probability. Under the objective options, choose Value Of and enter A2, or type the target value directly, such as 0.95. Set By Changing Variable Cells to B2. This tells Solver to change the z-score guess until its cumulative probability matches the target.
Choose a solving method and check the settings. Select GRG Nonlinear as the solving method. The cumulative normal function is smooth, so this method is appropriate. Make sure B2 is allowed to be negative: if Make Unconstrained Variables Non-Negative is checked, clear it. Otherwise, Solver may be unable to find a negative z-score for a target below 0.5. You generally do not need to add constraints for this calculation.
Run Solver and keep the solution. Select Solve. For a target of 0.95, Solver should find a z-score close to 1.64485 in B2, while C2 should be close to 0.95. Choose Keep Solver Solution in the results dialog, then select OK. The exact displayed digits can depend on the cell’s number format and Solver’s tolerance. Format B2 with additional decimal places if you need to see more of the result.
Check the result independently. Confirm that C2 matches A2 closely. You can also compare the answer with Excel’s inverse normal function. With the target probability in A2, the check formula is =NORM.S.INV(A2). It returns approximately 1.644853627 for A2 equal to 0.95. This direct function is usually quicker when you only need a z-score; Solver is useful when you need to demonstrate an optimization setup or include the probability calculation in a larger model.

Solving for a raw score instead: Sometimes the goal is to find a value in the original units, such as a test score, that corresponds to a percentile. Solver can adjust that raw value directly. Put the target cumulative probability in A2, the distribution mean in B2, the standard deviation in C2, and a starting raw score in D2. With that layout, enter =NORM.DIST(D2,B2,C2,TRUE) in E2. In Solver, set the objective to E2, choose Value Of A2, and set the changing variable cell to D2. For a target of 0.95, a mean of 100, and a standard deviation of 15, Solver should return a raw score close to 124.6728. The corresponding z-score is about 1.64485.

To turn that raw score into a z-score, with the solved raw score in D2, mean in B2, and standard deviation in C2, use =(D2-B2)/C2. For the example values, this returns approximately 1.64485. This distinction matters: Solver can find the score in original units, while the z-score expresses how many standard deviations that score is above or below the mean.

Common Mistakes

Entering a tail area as though it were cumulative. NORM.S.DIST with TRUE calculates area to the left. For an upper-tail area of 0.05, use a target of 0.95, not 0.05. If you enter 0.05, Solver correctly returns a negative z-score.
Using the density option. The second argument in NORM.S.DIST must be TRUE for cumulative probability. FALSE returns the height of the curve at z, not the area to the left, so it is not the right objective for this task.
Forgetting that Solver changes a cell. The changing variable must be the starting z cell, not the formula cell. The objective should be the cell that calculates the probability from that z value.
Leaving nonnegative variables enforced. A z-score may be negative. If Solver is restricted to nonnegative changing cells, it cannot reach a left-tail probability below 0.5.
Using a probability of exactly 0 or 1. A standard normal distribution reaches those cumulative probabilities only at negative or positive infinity. There is no finite z-score for either endpoint, so choose a probability strictly between 0 and 1.
Confusing standard deviation and variance. NORM.DIST requires the standard deviation, not the variance. If your data gives variance, take its square root before using it as the distribution’s standard deviation.

Tips

Label the cells clearly, for example Target probability, Starting z, and Calculated probability. Clear labels make Solver’s changing-cell and objective settings easier to verify.
Use a starting value near the likely answer. A guess of 0 is reasonable for probabilities near 0.5; for a very high cumulative probability, a positive guess can help Solver converge, and for a low probability, try a negative one.
Keep the target probability in its own cell instead of typing it only into the Solver dialog. It makes the model easier to update and lets you see which input the solution is matching.
Show enough decimal places in the result cell to make the answer useful. Formatting changes what you see, not the underlying value Solver calculated.
For an ordinary inverse-normal calculation, NORM.S.INV is simpler than Solver. Use Solver when you need to solve a broader model, find a raw score through a distribution formula, or practice setting a cell to a target value.

Troubleshooting

Solver is missing from the Data tab: Enable the Solver Add-in using the Excel Add-ins steps above. If the option is unavailable on a managed work computer, your organization may control add-ins; ask your Excel administrator. Excel for the web cannot run this desktop Solver add-in, so choose Open in Desktop App.

Solver reports that it cannot find a feasible solution: Check that the target is a number greater than 0 and less than 1, that the formula in C2 refers to B2, and that Solver is changing B2. Clear the nonnegative-variable option if the target is below 0.5. For the raw-score version, verify that the standard deviation is positive and that the formula references the correct mean and standard-deviation cells.

The result is close but not exact: Look at the difference between the objective and target at full precision, not just the rounded display. Confirm that GRG Nonlinear is selected, then run Solver again. If the workbook uses a very unusual starting guess, replace it with a reasonable value and solve again. You can also check the result with NORM.S.INV for the standard z-score case.

The answer has the wrong sign: Revisit whether your input is a left-tail cumulative probability or a right-tail area. A cumulative probability below 0.5 should produce a negative z-score; a cumulative probability above 0.5 should produce a positive one. Convert right-tail values before running Solver.

Solver changes the wrong cell or the result disappears: Reopen Data > Solver and confirm that the objective and changing-cell references are correct. When the Solver Results dialog appears, choose Keep Solver Solution rather than restoring the original values. If you want to try another target without losing a prior answer, copy the solved value elsewhere first.

Frequently Asked Questions

Can Excel calculate a z-score without Solver?
Yes. For a cumulative probability in A2, =NORM.S.INV(A2) directly returns its standard normal z-score. Solver is an alternative when you specifically need an adjustable-cell model or are solving for a raw value in a larger calculation.

What probability should I enter for the 95th percentile?
Enter 0.95 as the cumulative probability to the left. The resulting z-score is approximately 1.64485. Do not enter 95; probabilities in the formula and Solver setup should be decimals from 0 to 1.

How do I find the z-score for a 5% upper tail?
Convert the upper-tail area to a left-tail cumulative probability: 1 minus 0.05 is 0.95. Use 0.95 as the Solver target, which gives a positive z-score of about 1.64485.

How do I find both critical z-scores for a 95% two-sided interval?
Put 0.975 in the cumulative target to find the upper critical value, about 1.95996. The lower critical value is about -1.95996 because the standard normal distribution is symmetric. You can solve the lower value separately using a target of 0.025.

Can I use Solver to get a z-score from a non-normal distribution?
Only if you have a valid cell formula that calculates the cumulative probability for that distribution and Solver can adjust the input value. Solver does not make a distribution normal; the standard-normal steps here apply specifically to a normal model, and the raw-score example assumes a normal distribution with a specified mean and standard deviation.

Does this work in Excel for Mac?
The Solver add-in is available in desktop Excel for Mac, though add-in setup and dialog placement can vary. Use Tools > Excel Add-ins to enable Solver, then look for Solver on the Data tab. Excel for the web does not run this Solver workflow.

Try it: the Date Difference Calculator: days, months, years and weekdays between two dates, with the DATEDIF formulas.

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Sources: Function behaviour and menu paths: Microsoft Support documentation for Excel. Method & sources

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