Calculator Formulas

Flashcards for TMSCA Calculator and other mathematical purposes

Cube Volume

V = s^3

Cube Surface Area

SA = 6s^2

Cube Inner Diagonal

d = s * sqrt(3)

Rectangular Prism Volume

V = lwh

Rectangular Prism Surface Area

SA = 2(lw + lh + wh)

Rectangular Prism Space Diagonal

d = sqrt(l^2 + w^2 + h^2)

Square Area

A = s^2

Square Diagonal

d = s * sqrt(2)

Parallelogram Area

A = h*b

Triangle Area (General)

A = 0.5 * b * h

Triangle Area (45-45-90)

A = 0.5 * s^2

Triangle Area (30-60-90)

A = (sqrt(3)/4) * s^2

Scalene Triangle (Area)

A = 0.5 * a * b * sin(C)

Scalene Triangle (3 sides Area)

S= sides/2, A= sqrt((s)(s-a)(s-b)(s-c))

Equaliteral triangle

(side^2 x sqrt3) / 4

Law of Cosines

c^2 = a^2+b^2 - 2abCosc

Law of Sines

sina/a = sinb/b

Cone Volume

V = (1/3) * pi * r^2 * h

Cone Surface Area

SA = pi * r * (r + s)

Cone LSA

pi(r)(s)

Cone slant height

sqrt((r^2)+(h^2))

Frustum of Cone Volume

V = (pi * h/3) * (R^2 + R*r + r^2)

Frustum of Cone Surface Area

SA = pi * (R + r) * l + pi * (R^2 + r^2)

Cylinder Volume

V = pi * r^2 * h

Cylinder Surface Area

SA = 2 * pi * r * (r + h)

Cylinder Lateral SA

2pi(r)(h)

Sphere Volume

V = (4/3) * pi * r^3

Sphere Surface Area

SA = 4 * pi * r^2

Hemisphere Volume

V = (2/3) * pi * r^3

Hemisphere Surface Area

SA = 3 * pi * r^2

Tetrahedron Volume

V = (s^3) / (6 * sqrt(2))

Tetrahedron Surface Area

4(b*h/2)

Rhombus Area

A = 0.5 * d1 * d2

Circle Area

A = pi * r^2

Semi-Circle Area

A = 0.5 * pi * r^2

Ellipse Area

Pi * 1/2maj * 1/2min

Octagon Area (Regular)

A = 2 * (1 + sqrt(2)) * a^2

Hexagon Area (Regular)

A = (3 * sqrt(3)/2) * a^2

Regular Polygon (Longest Diagonal, even n)

side/sin(180/n)

Regular Polygon (Longest Diagonal, odd n)

side/ 2(sin 90/n)

Pentagon area

5/2 * ap * height

Pentagonal Prism Volume

(5/2) * a*b * h

Pentagonal Prism Surface Area

5 * a * h + (5/2) * a^2 * cot(pi/5)

All polygon area

perimeter^2/( (tan180/n)(4n) )

1 gallon

3.785 liters, 231 cubic inches

1 pint

16 fluid ounces

1 liter

1000 milliliters

1 foot

12 inches

1 yard

3 feet

1 mile

1.609 kilometers

1 meter

3.281 feet

1 pound

0.4536 kilograms

1 ton

2000 pounds

1 kilogram

1000 grams

Feet/sec to mph

(ft/s * 3600) / 5280

Simple Interest (I)

P * r * t

Compound Interest (A)

P * (1 + r/n)^(n*t)

Product of roots

c/a

Sum of roots

-b/a

Axis of symmetry

-b/2a

Harmonic mean

½)+(⅓)+(1/ number n)

Geometric mean

nroot(1x2xnumber)

Hexagonal numbers

(n(4n-2))/2

Pentagonal numbers

n(3n-1)/2

Discriminant

b^2-4ac

Explicit Geometric

An = A1 x R^n-1

Explicit arithmetic

An = A1 + (n-1)d

Sum of interior angles

(n - 2) * 180

Sum of exterior angles

360

Quadratic Formula

x = (-b +- sqrt(b^2 - 4ac)) / 2a

Vertex Formula

Vertex form: y = a(x-h)^2 + k , Vertex: (h,k)

Point Slope Formula

y - y1 = m(x - x1)