Grading scales, without hidden assumptions

Grade bands are policy, not math

GradCal ships with a simple default: A at 90%, B at 80%, C at 70%, D at 60%, and F below 60%. That is only a starting setup. Schools and teachers may use plus/minus tiers, standards-based labels, pass/fail, or different thresholds.

A band is represented as a label and an inclusive minimum. “B starts at 80” means a displayed score of exactly 80 belongs to B. Bands are evaluated from the highest minimum down, so overlapping definitions do not produce two answers.

Choose when rounding happens

This implementation calculates the raw percentage, applies the selected rounding rule, and then chooses the letter band. That order is explicit because it changes boundary results. For example, 89.96% rounds to 90.0% at one decimal and therefore reaches an A under the default bands. With no rounding, it remains below 90%.

The available modes are exact display, nearest whole number, nearest tenth, floor, and ceiling. “Floor” and “ceiling” are directional policies, not formatting: they change the value used for the band.

Half and quarter points

Partial credit changes the earned-points numerator, not the formula. A paper earning 8.5 out of 10 is 85%. In stack mode, the half-point button records a half-point deduction. The quick table can use whole, half, or quarter-point rows.

Use the smallest increment the rubric actually supports. Adding quarter-point rows to a whole-point test creates false precision without improving the decision.

Extra credit can exceed 100%

Extra credit is added to earned points before division. A student earning 20 points plus 2 bonus points on a 20-point assignment receives 110%. GradCal does not clamp that result to 100%, because doing so would hide the rule. If a school caps scores, apply that as an explicit policy outside the default contract.

Worked examples

Try these cases in the instant stack grader, or build a full easy grader table.

A short setup checklist

Start with the written grading policy rather than a preset name. Record the minimum percentage for every label, including the lowest band. Decide whether a boundary is inclusive, whether the displayed or raw percentage controls the letter, and which rounding mode applies. If a rubric permits partial credit, record the smallest point step that can actually be awarded. Finally, decide whether extra credit may push the assignment above 100% or whether an explicit cap applies.

Use the same setup for the entire stack. Changing a band or rounding rule halfway through creates results that look comparable but were produced under different policies. If a correction is required, update the setup and recalculate every paper in the session. A saved template is convenient, but the teacher remains responsible for confirming that it still matches the current syllabus, department rule, or school handbook.

When sharing a grade table, include the assignment total and rounding rule. A bare list of percentages can be misunderstood when another person expects exact values or a different boundary rule. GradCal’s anonymous CSV includes the numeric result and grade label, but it deliberately omits student identity and is not an official gradebook record.

Common questions

Should 89.5% become an A?

Only if the selected policy rounds 89.5% to 90% before band lookup. With exact grading, it stays below the 90% boundary. The important part is consistency, not choosing one convention universally.

What happens when the total is zero?

No grade is returned. Division by zero has no valid percentage interpretation, so GradCal treats a non-positive total as an error instead of displaying 0% or 100%.

Can earned points be greater than possible points?

Yes, through an explicit extra-credit value. The calculator keeps ordinary earned points and bonus points conceptually separate, adds them for the numerator, and shows a result above 100% when appropriate.

Does a grading scale calculate a course average?

No. A grading scale maps one percentage to a label. A course average may combine categories with different weights; that distinct job belongs in the weighted grade calculator.