ACT Math Calculators
One calculator for each formula on the enhanced ACT math test, grouped by reporting category, with exact answers, step-by-step working and the ACT score tools.
33 calculators · 5 converters · common conversions
Number and Quantity
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Complex Number Calculator
(a + bi)(c + di) = (ac − bd) + (ad + bc)i
i² = −1; divide by multiplying by the conjugate
Example: (3 + 4i) × (1 − 2i): Result = 11 − 2i.
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Matrix Calculator
det [[a, b], [c, d]] = ad − bc
A⁻¹ = (1/det) adj(A); no inverse when det = 0
Example: The matrix [[4, 7], [2, 6]]: Determinant = 10.
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- Simplify Radicals Calculator – A square or cube root → simplest radical form and its decimal value.
- Percent Calculator – P% of X, A as a percent of B, or the whole from a part and a percent.
- Ratio and Proportion Calculator – Solve a : b = c : x, or simplify a ratio to its lowest whole-number terms.
Algebra
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Linear Inequality Calculator
ax + b < c → x < (c − b)/a
the inequality sign reverses when dividing by a negative a
Example: The inequality −3x + 4 < 10: Solution = x > -2.
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Absolute Value Equation Calculator
|ax + b| = c ⇔ ax + b = c or ax + b = −c
no solution when c < 0; one solution when c = 0
Example: The equation |2x − 3| = 7: Solutions: x = -2 or x = 5.
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- Systems of Equations Calculator – Linear equations in two or three unknowns → exact solution, or a no / infinitely many solutions verdict.
- Quadratic Formula Calculator – a, b and c → roots (real or complex), discriminant, vertex, axis of symmetry and factored form.
- Slope-Intercept Form Calculator – Two points, or a point and slope → y = mx + b, standard form Ax + By = C and the x- and y-intercepts.
Functions
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Exponential Growth Calculator
y = a(1 ± r)ᵗ
a initial value, r rate per period, t periods; continuous: y = a·e^(±rt)
Example: 500 growing 8% per period for 5 periods: Value after t periods = 734.6640384.
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Logarithm Calculator
log_b(x) = ln x ÷ ln b
b^(log_b x) = x; bˣ = y ⇔ x = log_b y
Example: log base 2 of 64: log_2(64) = 6.
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- Arithmetic and Geometric Sequence Calculator – First term, difference or ratio and n → nth term, sum of n terms and the first few terms.
- Vertex Form Calculator – Standard form ↔ vertex form, with the vertex, maximum or minimum and y-intercept.
- Cubic Equation Calculator – Cubic coefficients → all roots (real or complex pair), with the sum and product of the roots.
Geometry
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Law of Sines and Cosines Calculator
a² = b² + c² − 2bc·cos A; a/sin A = b/sin B = c/sin C
area = ½bc·sin A
Example: A triangle with sides b = 8, c = 5 and angle A = 60° between them: Area = 17.32050808.
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Right Triangle Calculator
sin A = a/c, cos A = b/c, tan A = a/b
SOH-CAH-TOA; A + B = 90°
Example: A right triangle with legs 3 and 4: Hypotenuse c = 5.
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- Unit Circle Calculator – An angle → point on the unit circle, exact sin, cos and tan, reference angle and quadrant.
- Circle Equation Calculator – General form ↔ standard form (x − h)² + (y − k)² = r², with center, radius, area and circumference.
- Distance Formula Calculator – Two points → distance in simplest radical form and decimal.
- Midpoint Calculator – Two endpoints → midpoint, or one endpoint and the midpoint → the other endpoint.
- Special Right Triangles Calculator – One side of a 30-60-90 or 45-45-90 triangle → all sides in exact form, area and perimeter.
- Arc Length Calculator – Radius and central angle → arc length, sector area, chord and the angle in both units.
- Volume Calculator – Shape and dimensions → volume (with exact π form) and total surface area.
Statistics and Probability
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Mean, Median and Mode Calculator
mean = Σx ÷ n
median: middle value of the sorted data; mode: most frequent value; range = max − min
Example: The data 4, 8, 6, 5, 3, 8, 9, 5, 8: Mean = 6.222222222.
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Probability Calculator
P(A or B) = P(A) + P(B) − P(A and B)
independent: P(A and B) = P(A)P(B); P(A|B) = P(A and B)/P(B)
Example: Independent events with P(A) = 0.5 and P(B) = 0.4: P(A or B) = 0.7.
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- Permutation and Combination Calculator – n items, choose r → permutations, combinations and the with-repetition counts.
- Weighted Average Calculator – Values and their weights → weighted mean, with the unweighted mean for comparison.
- Standard Deviation Calculator – Paste a list of numbers → standard deviation, variance, mean, median, MAD and CV with steps.
- Binomial Distribution Calculator – Trials n, probability p and successes k → exact, cumulative and tail probabilities, mean and variance.
Scores and GPA
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ACT Score Calculator
Composite = round[(English + Math + Reading) ÷ 3]
.5 rounds up; STEM = round[(Math + Science) ÷ 2]
Example: English 30, Math 31 and Reading 32: ACT composite = 31.
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SAT to ACT Score Converter
Lookup in the 2018 ACT/SAT concordance table
each ACT composite corresponds to a range of SAT totals
Example: An SAT total of 1300: SAT 1300 ≈ ACT = 28.
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GPA Calculator
GPA = Σ(grade points × credits) ÷ Σ credits
A = 4.0, A− = 3.7, B+ = 3.3 … F = 0; AP/IB +1, Honors +0.5 for weighted
Example: Grades A (AP), A−, B+ (Honors), A (half credit) and B: Unweighted GPA = 3.556.
Unit Converters for ACT Math
- Angle Converter – degrees, radians, gradians, arcminutes
- Length Converter – m, km, cm, mm, µm, ft, in, mi, yd, nmi
- Area Converter – m², cm², mm², ft², in², test areas
- Volume Converter – L, mL, m³, ft³, in³, US gal, imp gal
- Speed Converter – km/h, mph, m/s, ft/s, knots
Common ACT Math Conversions
How to use these ACT math calculators
The enhanced ACT math test has 45 questions with four answer choices, and reports results in categories such as Number and Quantity, Algebra, Functions, Geometry, and Statistics and Probability. It covers a few topics the SAT rarely tests, including logarithms, matrices, sequences, complex numbers and the law of sines and cosines, which have their own calculators here.
You bring your own calculator to the ACT, so practise with the one you will use and set it to degree mode for geometry. These pages show each formula, the steps with your numbers and the exact answer, so you can check practice problems and learn which method is quickest.
The ACT composite is the average of English, Math and Reading, rounded to the nearest whole number; Science is optional and gives a separate STEM score. The score calculator applies that rule, builds a superscore from several test dates and shows the SAT equivalent from the official concordance.