Introduction: AllerCalc has more than one hundred functions, including algebraic, transcendental, trigonometric, hyperbolic, engineering, statistical, and financial functions. It performs numerical integration, differentiation, and root-finding. It comes preloaded with a list of common physical constants found in science and engineering. You can store results in an unlimited number of variables.
Box information and Reference
A cube is a three-dimensional figure with six matching square sides.
In a rectangular box, the length, width and height may be of different lengths.
l = length of box w = width of box h = height of box
You may assign values to variables which can then be used in subsequent calculations.
The variables will be saved when the program exits and may be re-used in subsequent sessions.
The following commands may be used with variables:
ShowVars: displays the variables' name and their values.
ClearVars: deletes the variables and their values.
fig. 1 Box Volume Volume = l*w*h
Surface Area = 2*(l*w+l*h+w*h)
fig. 2 Box Information and Reference Reference:
Online Rectangular Solid Calculator Reference:
Online Rectangular Prism Calculator
Pyramid Information and Reference A pyramid is a solid with a polygon base and connected by triangular faces to its vertex. A pyramid is a regular pyramid if its base is a regular polygon and the triangular faces are all congruent isosceles triangles.
l = length of base w = width of base h = height of pyramid
c and d = slant height of pyramid face (c= length face & d = width face)
AllerCalc has unlimited variable storage and more than 100 built-in math functions.
fig. 3 Pyramid Volume and Surface Area Volume = l*w*h/3
Surface Area = l*c+w*d+l*w
fig. 4 Pyramid Information and Reference Reference:
Online Rectangular Pyramid Calculator Reference:
Online Rectangular Pyramid Calculator Reference: Online Rectangular Pyramid Calculator
Topless Pyramid Information and Reference
A trunctated pyramid volume is one third the height times (A + sqrt(A*B) + B)
where A and B are the area of the top and bottom faces.
A= area (A*B) and B= area (C*D)
AllerCalc variables need not be only a character, "InterestRate" is a perfect name as well. And still, you can define as many variables as you want.
AllerCalc Topless Pyramid
fig. 5 Topless Pyramid Volume and Surface Area Volume = (h/3)((a*b)+(c*d)+√((a*b)(c*d)))
Surface Area = x+y+u u=(a*b)+(c*d)
x= 2*(a+c)*h/2 y= 2*(b+d)*h/2
fig. 6 Topless Pyramid Information & Reference Reference:
Online Topless Pyramid calculator Reference:
Online Geometric shapes Calculator Reference:
Online Truncated Pyramid Calculator
Cylinder Information and Reference A cylinder is a solid with two congruent circles joined by a curved surface.
The expression: v = π*r²*h:
AllerCalc does not use implied multiplication. For multiplication you need to include the multiplication operator. When an expression begins with an operator (+, -, *, /, %, or !), the previous calculation result is used as the first operand for the operator. Example:
+3 = (treated as ANS + 3, or 4 + 3)
r = radius of cylinder
h = height of cylinder
fig. 7 Cylinder Volume & Surface Area Volume = π*r²*h
Surface Area = 2*π*r(r+h)
Note: 2πr*(r+h) = 2*πr² + 2*π*r*h
fig. 8 Cylinder Information & Reference Reference:
cylinder volume Reference:
cylinder formulas Reference:
cylinder surface area
Cone Information and Reference A circular cone has a circular base, which is connected by a curved surface to its vertex.
The vertex is the top or pointed area of the cone.
r = radius of cone base
h = height of cone
l = slant height of cone (see diagram)
l = √(r²+h²)
Total Surface Area = Lateral Surface Area + Base Area
Lateral Surface Area = π*r*√(r²+h²)
Base Area = π*r²
Total Surface Area = π*r²+π*r*√(r²+h²)
fig. 9 Cone Volume and Surface Area Volume = π*r²*h/3
Surface Area = π*r²+π*R√(R²+h²)
fig. 10 Cone Information and Reference Reference:
Cone formulas Reference:
Topless Cone Information and Reference
L= Lateral Surface Area:
A= Total Surface Area
Topless Cone = Cone Frustum
Topless Cone = Truncated Cone
fig. 11 Topless Cone Volume Volume = πh/3(R1²+R2²+R1R2)
Surface Area = π(R1+R2)√((R1-R2)²+h²)+π(R1²+R2²)
fig. 12 Topless Cone Information & Reference Reference:
Truncated Cone Reference:
Sphere Information and Reference
A sphere is a solid with all its points equal distance from the center.
r = radius of sphere
In AllerCalc you just type the expression that you want to calculate and press Enter. You can see clearly what you typed along with the result in the scrollable display.
fig. 13 Sphere Volume and Surface Area Volume = 4/3πr³
Surface Area = 4πR²
fig. 14 Sphere Information and Reference Reference:
Sphere Calculator Reference:
Sphere 2 Base Segment Information and Reference
a= large radius of segment
b= small radius segment
h= height of segment
R= radius of sphere
AllerCalc Sphere 2 Base Segment
fig. 15 Sphere 2 base segment Volume and Surface Area Volume = (π/3)h²(3R-h)
Surface Area = 2πRh
fig. 16 Sphere 2 base segment Information and Reference Reference:
Volume of a Spherical Segment Reference:
Surface Area of a Spherical
Spherical Lune/Wedge Volume and Surface Area Spherical Wedge the portion of a sphere included between two planes which intersect at the diameter.
portion of the surface of a sphere included between two great semicircles having a common diameter.
A Spherical Lune is the surface area of a Spherical Wedge.
a = angle in degrees
Ref: Sphere formulas
Ref: Spherical wedge formulas
Ref: Spherical wedge formulas
AllerCalc Spherical Lune/Wedge
fig 17 Spherical Lune/Wedge Volume and Surface Area Volume Spherical Wedge= (π/270)r³θ
Surface Area Spherical Lune= (π/90)r²θ
fig 18 Spherical Lune/Wedge Information and Reference Reference:
Volume of a Spherical Wedge in degrees Reference:
Surface Area of a Spherical Lune in degrees
Spherical Cap Information and Reference
In geometry, a spherical cap is a portion of a sphere cut off by a plane.
The expression: A = 2*π*r*h:
R = radius of sphere
h = height of cap
a = radius of the cap (or plane)
AllerCalc Spherical Cap
fig. 19 Spherical Cap Volume and Surface Area Volume = πh²(3R-h)/3
Surface Area = 2πRh
fig. 20 Spherical Cap Information and Reference Reference:
Spherical Cap Calculator Reference:
Spherical Sector Information and Reference
The part of a sphere between two right circular cones that have a common vertex
at the center of the sphere, and a common axis.
AllerCalc Spherical Sector
fig. 21 Spherical Sector Volume and Surface Area Volume = (2/3)πR²h
Surface Area = 2πRh
fig. 22 Spherical Sector Information and Reference Reference:
Spherical Sector Reference:
fig. 1/fig. 2 Box Volume and Surface Area 'Box
L=6, W=5, H=4
fig. 3/fig. 4 Pyramid Volume and Surface Area 'Pyramid
W=5, L=6, H=5
fig. 5/fig. 6 Topless Pyramid Volume and Surface Area 'Topless Pyramid
a=6, b=5, h=4, c=3. d=2.5
fig. 7/fig. 8 Cylinder Volume and Surface Area 'Cylinder
fig. 9/fig. 10 Cone Volume and Surface Area 'Cone
fig. 13/fig. 14 Sphere Volume and Surface Area 'Sphere
noun, plural frus•tums, frus•ta /Geometry.
1. the part of a conical solid left after cutting off a top portion with a plane parallel to the base.
1. Having the apex (top portion) cut off and replaced by a plane, especially one parallel to the base. Used of a cone or pyramid.
n. pl. ver•ti•ces (-t-sz) also ver•tex•es
1. The highest point; the apex or summit: the vertex of a mountain.
Mathematical References and Formulas:
1300 Math Formulas Textbook on Math Formulas - Number Sets, Algebra, Geometry, Trigonometry, Matrices and Determinates, Vectors, Analytic Geometry, Differential Calculus, Integral Calculus, Differential Equations, Series, Probability
Geometric Shapes in Solid Geometry Shape diagrams and formulas for geometric solids including capsule, cone, conical frustum, cube, cylinder, hemisphere, pyramid, rectangular prism, sphere.
Handbook of Mathematics Calculator Operations, Calculator Usage, Special Keys, Algebra, Geometry, Trigonometry, Higher Concepts of Mathematics
SAT Test - Math
SparkNotes SAT Polygons Good news: Most polygons on the SAT have just four sides. You won’t have to tangle with any dodecahedrons on the SAT you take. There are five different types of quadrilaterals that pop up on the test. These five quadrilaterals are trapezoids, parallelograms, rectangles, rhombuses, and squares.
SparkNotes SAT Circles A circle is the collection of points equidistant from a given point, called the center. A circle is named after its center point. The distance from the center to any point on the circle is called the radius, (r), the most important measurement in a circle.
SparkNotes SAT Triangles Triangles pop up all over the Math section. There are questions specifically about triangles, questions that ask about triangles inscribed in polygons and circles, and questions about triangles in coordinate geometry.
SparkNotes SAT Algebra
Free Math eBooks:
The Handbook of Essential Mathematics 205 pages of mathematical formulas and other useful technical information that will serve both students and teachers. A pdf file.
A First Book in Algebra by Wallace C. Boyden In preparing this book, the author had especially in mind classes in the upper grades of grammar schools
Algebra for Beginners Contents: Addition; Subtraction; The use of Double Signs and Brackets; Multiplication; Division; Simple Equations; The Lowest Common Multiple; Fractions; Quadratic Equations; Simultaneous Equations; Exponential Notation.
Algebra I an introduction to algebraic concepts for the high school student. Topics include: Equations and Functions, Real Numbers, Equations of Lines, Solving Systems of Equations and Quadratic Equations.
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