Engineering calculation examples
Free, unit-aware calculation worksheets across structural, mechanical, electrical and more. Open any example into your own workspace to edit and reuse. New to Calculeaf? Start with your first worksheet or the examples guide.
Often opened: beam deflection formulas, bolt stiffness, pressure vessel wall thickness, ASME B31.8 pipe wall thickness, pressure drop in a pipe, weight from mass.
21 examples found
Quadratic Formula Roots
Real roots of a quadratic equation and its discriminant via the quadratic formula.
Pythagorean Theorem (Ladder)
Length of a ladder reaching a height against a wall via the Pythagorean theorem.
Triangle Area by Heron’s Formula
Area of a triangle from its three side lengths using Heron’s formula.
Circle Circumference
Circumference of a circle from its radius.
Sphere Volume
Volume of a sphere from its radius.
Sphere Surface Area
Surface area of a sphere from its radius.
Cone Volume
Volume of a right circular cone from its base radius and height.
Trapezoid Area
Cross-sectional area of a trapezoid, e.g. an embankment or channel.
Compound Interest
Future value of a principal under annual compound interest.
Roof Pitch Angle
Slope angle of a roof or ramp from its rise and run.
Distance Between Two Points
Straight-line distance between two points from their coordinates.
Mean and Standard Deviation of a Data Set
Sample mean and sample standard deviation of five measured values, computed from first principles.
Standard Normal Z-Score
Converts a raw measurement into standard deviations from the mean (a z-score) for comparison against a normal distribution.
Linear Regression Slope and Intercept (Least Squares)
Best-fit straight line through four data points using the ordinary least-squares normal equations.
Sample Size for a Target Margin of Error
Minimum survey sample size needed to achieve a specified margin of error at a given confidence level.
Permutations and Combinations Count
Number of ordered arrangements (permutations) and unordered selections (combinations) of r items chosen from n.
2×2 Matrix Determinant
Determinant of a 2×2 matrix computed from its four scalar entries.
Vector Dot Product and Angle Between Two Vectors
Dot product of two 3D vectors given by components, and the angle between them.
Vector Cross Product Magnitude
Cross product of two 3D vectors given by components, and the magnitude of the resulting vector.
Arithmetic Series Sum
Sum of the first n terms of an arithmetic sequence with a given first term and common difference.
Geometric Series Sum
Sum of the first n terms of a geometric sequence with a given first term and common ratio.