SolvexCalc

Math calculators

From a single quadratic equation to a full scientific calculator, this page covers the math tools people reach for most — solving equations, summarizing a data set, converting grades, and everything in between. Every result comes with the formula and a worked example, so you can check the logic, not just copy a number.

Quadratic equation solver

Solve ax² + bx + c = 0 for real or complex roots.

Roots
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Enter coefficients a, b, c.

How this calculator works

Any quadratic equation of the form ax² + bx + c = 0 can be solved with the quadratic formula. The expression under the square root, b² − 4ac, is called the discriminant — its sign tells you what kind of roots to expect before you even finish the calculation.

x = (−b ± √(b² − 4ac)) / 2a
Worked example: For x² − 3x + 2 = 0 (a=1, b=−3, c=2): discriminant = (−3)² − 4×1×2 = 9 − 8 = 1. Since it's positive, there are two real roots: x = (3 ± 1) / 2, giving x = 2 and x = 1.
  • Discriminant > 0 — two distinct real roots (the graph crosses the x-axis twice).
  • Discriminant = 0 — exactly one real root (the graph touches the x-axis at its vertex).
  • Discriminant < 0 — two complex roots of the form p ± qi (the graph never crosses the x-axis).

Mean & median calculator

Paste a list of numbers separated by commas to get quick statistics.

Summary
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Enter a list of numbers.

How this calculator works

Mean and median are both "averages," but they answer slightly different questions. The mean sums every value and divides by the count, so it's sensitive to extreme outliers. The median is simply the middle value when the data is sorted — or the average of the two middle values for an even-sized list — making it more resistant to unusually large or small numbers.

Mean = (sum of all values) / (count of values)
Median = middle value of sorted data (or average of the two middle values)
Worked example: For the list 4, 8, 15, 16, 23, 42: mean = (4+8+15+16+23+42)/6 = 108/6 = 18. Sorted, the two middle values are 15 and 16, so median = (15+16)/2 = 15.5.

When mean and median differ a lot, it's usually a sign of skewed data — for example, average household income is typically much higher than median income because a small number of very high earners pull the mean upward.

GPA calculator

Enter letter grades and credit hours for up to 6 courses to get your weighted GPA.

Weighted GPA
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Enter grades and credit hours above.

How this calculator works

A weighted GPA accounts for the fact that a 4-credit course should count more toward your overall average than a 1-credit course. Each letter grade is first converted to grade points on a 4.0 scale, multiplied by that course's credit hours, then all the results are summed and divided by the total credit hours.

GPA = Σ(grade points × credit hours) / Σ(credit hours)
Worked example: An A (4.0) in a 4-credit class and a B (3.0) in a 3-credit class: (4.0×4 + 3.0×3) / (4+3) = (16 + 9) / 7 = 25/7 ≈ 3.57 GPA — closer to the A than a simple unweighted average would suggest, because the A came from more credit hours.

Grade point scales vary between schools — some use A- = 3.7 and B+ = 3.3 as shown here, while others round differently or don't use +/− grades at all. Always confirm your institution's exact scale for an official transcript GPA.

Percentage-to-letter-grade converter

Convert a numeric score to a standard US letter grade.

Letter grade
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Enter a score between 0 and 100.

How this calculator works

This tool maps a percentage score onto the standard US letter-grade scale, where each letter corresponds to a range of percentages. It's the same scale used on most report cards and syllabi in the United States, though the exact cutoffs can vary by school or instructor.

90–100% → A · 80–89% → B · 70–79% → C · 60–69% → D · Below 60% → F
(with +/− subdivisions typically at the top and bottom 3 points of each range)
Worked example: An 88% score falls in the 80–89% range, so it converts to a B — specifically a B+ under most +/− schemes, since 88 sits in the upper part of that range.

Some institutions use a stricter or more lenient scale (for example, requiring 93%+ for an A), and some don't use +/− grades at all — check your specific syllabus if the exact cutoff matters for your grade.

Scientific calculator

Trigonometric & logarithmic functions, memory, constants, and degree/radian modes.

 
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Trig functions use the DEG/RAD mode shown above the display. Tap the mode badge to switch.

How this calculator works

This is a full scientific calculator supporting trigonometry, logarithms, powers, roots, and memory storage, evaluated left-to-right with standard parentheses grouping. The DEG/RAD toggle controls how trig functions interpret their input — degrees (0–360°) or radians (0–2π).

  • sin / cos / tan — trigonometric functions, using whichever angle mode (DEG or RAD) is currently selected.
  • ln / log — natural logarithm (base e) and common logarithm (base 10).
  • x² / x³ / xʸ / √ — square, cube, arbitrary power, and square root.
  • M+ / M− / MR / MC — add to memory, subtract from memory, recall stored value, and clear memory.
Worked example: In DEG mode, sin(30) = 0.5, matching the well-known triangle ratio. Switching to RAD mode, sin(30) instead computes sine of 30 radians (≈ −0.988), since 30 radians is a much larger angle than 30 degrees — this is the most common source of confusion when a scientific calculator gives an unexpected result.

Constants π and e are inserted as their full-precision values, so results involving them (like 2×π) carry full floating-point accuracy rather than a rounded approximation.

Frequently asked questions

What does the quadratic solver do with complex roots?

When the discriminant (b²-4ac) is negative, the equation has no real solutions. The calculator shows the complex roots in the form a ± bi.

Is the GPA calculator based on a 4.0 scale?

Yes, it uses the standard US 4.0 unweighted scale. Some schools use different scales or weight honors/AP courses differently — check with your institution for official calculations.

Why do sin/cos/tan give different answers in DEG vs RAD mode?

Degrees and radians are two different units for measuring the same angle — 180° equals π radians. If your calculator is in the wrong mode for your input, the result will be mathematically correct for that mode but not for what you intended, which is why checking the DEG/RAD badge before a trig calculation matters.

What's the difference between mean, median, and mode?

Mean is the sum divided by the count. Median is the middle value when sorted. Mode is the most frequently occurring value in the data set — this calculator computes mean and median, since mode requires repeated values to be meaningful and isn't always defined for a data set.

Can a quadratic equation have more than two solutions?

No — a quadratic (degree 2) polynomial has at most two roots, whether real or complex, by the fundamental theorem of algebra. If a appears to be 0, the equation is actually linear (bx + c = 0), not quadratic, and has at most one solution.

Why does my letter grade differ from what my school reports?

Grading scales aren't universal — some schools set the A cutoff at 90%, others at 93% or 94%, and some don't use +/− subdivisions at all. This calculator uses the most common US convention, but always defer to your syllabus or institution's official scale.

What does log(x) mean if x is zero or negative?

Logarithms are only defined for positive numbers — log(0) is undefined (it approaches negative infinity as x approaches 0), and the logarithm of a negative number is not a real number. Entering zero or a negative value into ln or log will produce an error or "Error" result.

Does the calculator follow standard order of operations?

Yes — multiplication and division are evaluated before addition and subtraction, exponents before both, and anything inside parentheses is evaluated first, following the same PEMDAS/BODMAS rules taught in school math.