Mathematics calculators
GCD, circle area, percent, volumes and sequences. Each calculator keeps its own formula on its own page.
Geometry
Annulus area calculator
A=π(R²−r²); R=2, r=1 → ≈9.42.
Use calculator →Arc Length Calculator
L = r·θ; 180° and r = 1 → π; degrees or radians.
Use calculator →Arccos Calculator
arccos(0.5)=60°; arccos(0)=90°; domain [−1,1], range [0°,180°].
Use calculator →Arcsin Calculator
arcsin(0.5)=30°; arcsin(1)=90°; domain [−1,1], range [−90°,90°].
Use calculator →Arctan Calculator
arctan(1)=45°; arctan(√3)=60°; domain ℝ, range (−90°, 90°).
Use calculator →Circle Circumference Calculator
C = 2πr = πd: at r = 10 ≈ 62.83 (radius or diameter).
Use calculator →Circle sector area calculator
A=½r²θ; 90° and r=2 → π.
Use calculator →Circle segment area calculator
A=(r²/2)(θ−sinθ); r=2, 90° → ≈1.14.
Use calculator →Cotangent Calculator
cot(45°)=1; cot(30°)=√3; undefined at 0° (sin = 0).
Use calculator →Cylinder volume from circumference
V = C²h/(4π); 2×4 → 1.27; ≈31.4×10 → 785.
Use calculator →Distance from point to line calculator
d=|Ax₀+By₀+C|/√(A²+B²); (0,0) and 3x+4y+5=0 → 1.
Use calculator →Equilateral triangle area calculator
A=½·a·h; a=10, h=6 → 30.
Use calculator →Equilateral Triangle Height Calculator
h=(√3/2)·a; a=2→√3≈1.732; a=6→≈5.196.
Use calculator →Law of Cosines Calculator
c=√(a²+b²−2ab cos γ); 3,4,90°→5; 7,8,120°→13.
Use calculator →Law of Sines Calculator
b=a·sin(β)/sin(α); 10,30°,90°→20. AAS/ASA.
Use calculator →Polygon diagonals calculator
n=4→2; n=5→5; n=6→9; D = n(n−3)/2.
Use calculator →Parallelogram area calculator with sine
A=a·b·sin(γ); 4×5×30° → 10.
Use calculator →Triangle Angle Calculator
γ=180°−α−β; 60°+60°→60°, 90°+45°→45°.
Use calculator →Polygon Interior Angle Sum Calculator
S=(n−2)×180°; n=3 → 180°, n=6 → 720°.
Use calculator →Algebra
Decimal to Fraction Calculator
0.75 = 3/4; 0.125 = 1/8; GCD reduce ≤ 10,000.
Use calculator →Fraction Calculator
1/2+1/3=5/6; 3/4×2/5=3/10; GCD reduce.
Use calculator →Absolute Value Calculator
|−7|=7; |12.5|=12.5; |0|=0. Reals only.
Use calculator →Ceiling Function Calculator
⌈3.2⌉=4; ⌈−1.2⌉=−1. Toward +∞, not floor.
Use calculator →Common logarithm calculator
log₂(8)=3; log₁₀(1000)=3; number then base.
Use calculator →Difference of squares a² − b²
a²−b²; a=5, b=3 → 16.
Use calculator →Exponential Function Calculator
e¹ ≈ 2.718; e⁰ = 1; e² ≈ 7.389; base e.
Use calculator →Floor Function Calculator
⌊3.7⌋=3; ⌊−1.2⌋=−2; greatest integer ≤ x.
Use calculator →Fractional Part Calculator
{3.75}=0.75; {−1.3}=0.7; formula x−⌊x⌋ in [0, 1).
Use calculator →Fractional exponents calculator
x^(m/n); 8^(2/3)=4; 27^(2/3)=9.
Use calculator →Hyperbolic Cosine Calculator
cosh(0)=1; cosh(1)≈1.543; formula (eˣ+e⁻ˣ)/2, result ≥ 1.
Use calculator →Hyperbolic sine calculator
sinh(x); sinh(1)≈1.175201.
Use calculator →Hyperbolic Tangent Calculator
tanh(x); tanh(0)=0, tanh(1)≈0.761594.
Use calculator →Linear Function Value Calculator
y=a·x+b; 2,3,4→11. Not from two points.
Use calculator →Linear Interpolation Calculator
(0,0)–(10,10), x=5 → y=5; lerp; extrapolation OK.
Use calculator →Logarithm to any base
log₂(8)=3; log₁₀(100)=2; ln(x)/ln(a).
Use calculator →Maximum of two numbers calculator
max(3,7)=7; max(−2,5)=5; (a+b+|a−b|)/2.
Use calculator →Minimum and maximum calculator
3,7,5 → 3/7/4; range = max − min.
Use calculator →Natural logarithm calculator
ln(e)=1; ln(1)=0; ln(20)≈2.996; x>0.
Use calculator →Nth root calculator
ⁿ√x; ∛27=3, √16=4.
Use calculator →Percentage change calculator
(new−old)/|old|; −25→25=+200%.
Use calculator →Ratio of Two Numbers Calculator
12:8 → 3:2 (GCD=4); 45:15 → 3:1.
Use calculator →Round to n Decimal Places Calculator
3.14159→3.14; 2.5→3; 1.005→1.00. Not Excel −k.
Use calculator →Map Scale Calculator
1:N; 2 cm at 1:50,000 → 1 km.
Use calculator →Signum Function Calculator
sgn(5)=1; sgn(−3)=−1; sgn(0)=0. Not |x|.
Use calculator →Square of a sum (a + b)²
(3+4)²=49; (5+3)²=64; a² + 2ab + b².
Use calculator →Statistics
Attendance Calculator
80/100 = 80%; 75% threshold → how many left to miss.
Use calculator →Geometric Mean Calculator
√(a·b); 4 and 9 → 6, 2 and 8 → 4.
Use calculator →Harmonic Mean Calculator
H=2ab/(a+b); 3 and 6 → 4, 60 and 90 → 72.
Use calculator →Median of five numbers calculator
1,5,3,4,2 → 3; 1,2,3,4,100 → 3.
Use calculator →Permutation calculator
P(n)=n!; P(5)=120, P(0)=1.
Use calculator →Range calculator
List → R=max−min; 2,5,8,11 → 9.
Use calculator →Standard deviation calculator (3 numbers)
σ /3; 1,2,3 → 0.816; 2,2,2 → 0.
Use calculator →Variance Calculator
σ²=SSD/n; 1–5→2. Population ÷n.
Use calculator →Other
Roman Numeral Converter
2026→MMXXVI; 14→XIV; range 1–3999, subtractive notation.
Use calculator →GPA Calculator
A+B at 3 cr → 3.50; scale 4.00/4.30; not ECTS.
Use calculator →ECTS Weighted Average Calculator
Σ(grade×ECTS)/Σ(ECTS); 5 and 3 at 6 → 4.00.
Use calculator →Random Number Generator
Inclusive integers; 1–6 P=1/6; no-repeats option.
Use calculator →Average Calculator
2 4 6 → 4; an outlier like 1000 pulls the mean.
Use calculator →Arithmetic sequence nth term calculator
aₙ = a₁+(n−1)r; 1,2,5 → 9; 3,5,4 → 18.
Use calculator →Arithmetic Series Sum Calculator
Sₙ=n·(a₁+aₙ)/2; 3 and 21, n=7 → 84.
Use calculator →Circle Area Calculator
A = πr²: at r = 10 ≈ 314.16 (radius, not diameter).
Use calculator →Combinations Calculator
C(5,2)=10; C(10,3)=120; order ignored.
Use calculator →Cone volume calculator
V = (1/3)·π·r²·h; 5×12 → 314.16; 3×9 → 84.82.
Use calculator →Cosine Calculator
sin 30°=0.5; sin 90°=1; sides 3/5→0.6.
Use calculator →Cube volume calculator
V = a³; 4 → 64; 5 → 125; 10 → 1000.
Use calculator →Cylinder lateral area calculator
Sb=2πrh; r=5, h=12 → 376.99.
Use calculator →Cylinder Volume Calculator
V = πr²h: at r = 5 and h = 10 ≈ 785.40 (radius and height).
Use calculator →Distance between two points calculator
d=√(Δx²+Δy²); (0,0)–(3,4) → 5.
Use calculator →Ratio Split Calculator
100 in 3 : 2 → 60 and 40; formula S×a/(a+b).
Use calculator →Ellipse area calculator
A=π·a·b; a=10, b=6 → ≈188.50.
Use calculator →Factorial calculator
n!; 5!=120, 0!=1, 7!=5040.
Use calculator →GCD Calculator
GCD(48, 18) = 6; GCD(17, 13) = 1 — two integers.
Use calculator →Geometric sequence nth term calculator
aₙ = a₁·qⁿ⁻¹; 2,3,4 → 54; 1,2,5 → 16.
Use calculator →Geometric Series Sum Calculator
Sₙ=a₁(1−qⁿ)/(1−q); 2,3,4 → 80.
Use calculator →LCM Calculator
LCM(6, 8) = 24; LCM(4, 6) = 12 — two integers.
Use calculator →Linear equation calculator
ax+b=0; a=2, b=6 → x=−3.
Use calculator →Logarithm calculator
Logarithm calculator: the base and the number.
Use calculator →Median Calculator
12 7 9 3 18 → 9; even 4 10 2 8 → 6. Middle value after sorting.
Use calculator →Midpoint Calculator
M=((x1+x2)/2,(y1+y2)/2); (0,0)–(4,6) → (2,3).
Use calculator →Modulo (remainder) calculator
17 mod 5 = 2; 10 mod 3 = 1; 8 mod 4 = 0.
Use calculator →Parallelogram area calculator
A=a·h; a=8, h=5 → 40.00.
Use calculator →Percentage change calculator
80→100 = +25%; 100→80 = −20%.
Use calculator →Percentage Calculator
15% of 200 = 30; 20% of 150 = 30 — also what % and after change.
Use calculator →Exponent calculator
a^b; 2^10=1024; 2^−3=0.125.
Use calculator →Prism volume calculator
V = B·h; 24×10 → 240; 36×5 → 180.
Use calculator →Pyramid volume calculator
V = (1/3)·B·h; 36×9 → 108; 24×6 → 48.
Use calculator →Pythagorean Theorem Calculator
a² + b² = c²: with 3 and 4, c = 5 (solve for a, b, or c).
Use calculator →Quadratic equation calculator
ax²+bx+c=0; x²−5x+6 → 2 and 3.
Use calculator →Rectangle area calculator
A=a·b; a=10, b=5 → 50.00.
Use calculator →Rhombus area calculator
A=e·f/2; e=6, f=8 → 24.00.
Use calculator →Rule of three calculator
x=(b×c)/a; 2→5, c=6 → 15.
Use calculator →Sine calculator
Pick from an angle or from triangle sides (sine angle).
Use calculator →Sphere surface area calculator
S=4πr²; r=10 → ≈1256.64.
Use calculator →Sphere Volume Calculator
V = (4/3)πr³: at r = 10 ≈ 4188.79 (radius, not diameter).
Use calculator →Square Root Calculator
√81 = 9; √144 = 12; √2 ≈ 1.414 — non-negative x only.
Use calculator →Standard deviation calculator
σ /n; 2 and 8 → 3; list → 2.
Use calculator →Degrees to Radians Calculator
°×π/180; 180°=π, 90°=π/2. Also rad→°.
Use calculator →Tangent Calculator
tan 45°=1; from angle or sides 3/4=0.75.
Use calculator →Trapezoid area calculator
A=½(a+b)·h; 10,6,4 → 32.
Use calculator →Triangle area calculator
Triangle area calculator: the base and the height perpendicular to it.
Use calculator →Heron's formula calculator
A=√[s(s−a)(s−b)(s−c)]; 3-4-5 → 6.
Use calculator →Variations Calculator
V(5,3)=60; V(10,3)=720. No repetition.
Use calculator →Vector Magnitude Calculator
‖(3,4)‖=5; ‖(3,4,12)‖=13. Empty z=2D.
Use calculator →Weighted Average Calculator
Weighted average: a value and a weight.
Use calculator →Grade Calculator
42 of 50 → 84% and a B; also weights and final need.
Use calculator →Articles
Short guides for the formulas in this category. Each article leads to a calculator.