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1. Thus, the difference quotient can be interpreted as instantaneous velocity or as the slope of a tangent to a curve. It was the calculus that established this deep connection between geometry and physics—in the process transforming physics and giving a new impetus to the study of geometry.
2. Lauren Lynn MacKenzie Class of 2006. This year I welcomed my first baby. His name is Wyatt Douglas MacKenzie and he was born on 2/22/18. Meghan Lohkemper Bergmann.

We have partnered with Mathway to offer a free online calculus calculator. An extensive list of other calculus tools is located below.

Table of Contents

• 48 Intro to Calculus Calculators
• 40 Advanced Calculus Calculators

Overview

At its core, MIT's Department of Mathematics explains, calculus is “the study of how things change.” It is an important area of study, the department notes, because “it provides a way for us to construct relatively simple quantitative models of change, and to deduce their consequences.”

There are many resources available online to help you learn more about calculus and its concepts. Following is a collection of 88 calculators separated by skill level and type.

48 Intro to Calculus Calculators

Limits

Learning about limits will be an essential part of your calculus study, since they address the value the function approaches as the input approaches a certain value. Khan Academy provides lessons on what limits are and how they work. Below is a collection of resources to help you better understand limits:

WolframAlpha.com's Limit – The results include your limit, the limit plotted on a graph, and the series expansion.

Symbolab.com's Limit – Cleanly designed and easy to use, results include a step-by-step explanation and the option to see your limit on a graph.

MathPortal.org's Limit – Enter your function and check whether you'd like to find the two-sided, left-hand or right-hand limit. Then, clear results are provided.

NumberEmpire.com's Limit – Input your own function or try one of the examples, and get quick and comprehensible results.

SolveMyMath.com's Limit – Simple to use; enter your function to find the two-sided, left, or right limit.

Calcul.com's Limit - Enter your expression and the limit will be provided.

4 Asymptote Calculators

MathIsFun.com teaches that an asymptote is “a line that a curve approaches, as it heads towards infinity.” Below is a collection of tools to help familiarize you with asymptotes.

WolframAlpha.com's Asymptotes – Use the drop down menu to choose which asymptote you want to find, either oblique, horizontal, or vertical.

Symbolab.com's Asymptotes – Enter your own function or choose one of the examples. Results include brief explanations and your graphed asymptote.

EasyCalculation.com's Asymptotes – Each of these tools includes the different possible methods used for solving asymptotes. Just enter your equation and results include asymptote point as well as the graphed asymptote.

Derivatives

As SOSMath.com explains, a derivative is often defined in two ways either as “a slope of a curve” or as “a rate of change.” Below is a collection of resources to help you learn more about derivatives:

SolveMyMath.com's Derivative – Try one of the examples or enter your own expression. A graph of the derivative is provided with your results.

Calculus-Calculator.com's Derivative – Simple to use and provides a step-by-step explanation along with your results.

WolframAlpha.com's Derivative – Learn more about derivatives from the detailed tutorial information. Results include your graphed derivative, its series expansion, its indefinite integral, and more.
Derivative-Calculator.net's Derivative – Straightforward with a step-by-step explanation given alongside your results.
Symbolab.com's Derivative – Cleanly designed and easy to use, you can either enter your own expression or use one of the examples to learn more about derivatives. A step-by-step explanation is provided with results.

MathPortal.org's Derivative – Follow the guided directions to ensure you enter your expression correctly. The first, second, or third derivative can be provided.

WebMath.com's Find a Derivative – Tutorial information is provided and the results include a step-by-step explanation.

Calc101.com's Step-By-Step Derivatives – Includes a step-by-step explanation of how to find the first and second derivative is provided.
EasyCalculation.com's Derivative – Follow the instructions provided to ensure you enter your expression correctly.

PlanetCalc.com's Derivative – To learn more about derivatives, check out the provided differentiation rules and derivatives of common functions.

Calcul.com's Derivative – Enter your expression and the derivative will be provided.

Saltire.com's Derivative – Enter your function and the results will be shown on a graph.

Product Rule

EasyCalculation.com explains that the product rule is a “method of finding the derivative of a function that is the multiplication of two other functions for which derivatives exist.” Below are two tools that use the product rule to find a derivative:

WolframAlpha.com's Product Rule – Very simple to use, just enter your function and the result is given.

EasyCalculation.com's Product Rule – Enter your own function or use one of the built-in examples. The product rule is used to provide your results.

Quotient Rule

As explained by the University of California Davis' Mathematics Department the quotient rule is “a formal rule for differentiating problems where one function is divided by another.”

EasyCalculation.com's Quotient Rule – Some tutorial information is provided to help you better understand this rule. Enter your own function or try one of the examples provided to further illustrate.

WolframAlpha.com's Quotient Rule – Enter the numerator and denominator to find the derivative of your function using the quotient rule.

Rates of Change

MathWords.com notes that a rate of change is “the change in the value of a quantity divided by the elapsed time.” Below are tools to help you learn more about finding rates of change.

TutorVista.com's Average Rate of Change – Use the provided step-by-step explanations to learn more about how to find the rate of change.

WolframAlpha.com's Average Rate of Change – Fast, easy to use, and provides clear results.

Taylor Expansion Series or Taylor Polynomial

As MathIsFun.com explains, a Taylor Series is “an expansion of a function into an infinite sum of terms.” Below are resources to help you learn more about Taylor series, a concept that often trips up calculus students when first encountered.

WolfamAlpha.com's Taylor Series – Examples are provided to show how to use this tool to perform series expansions based on certain criteria. Results include the series expansion, a graphed visual aid, and more.

NumberEmpire.com's Taylor Series – Includes brief tutorial information. Use one of the four examples or enter your own function. User-friendly results and the option to see a graphed representation are provided.

SolveMyMath.com's Taylor Series Expansion – Basic tool that provides clear results.

Inflection Points

As Wolfram MathWorld explains an inflection point is “a point on a curve at which the sign of the curvature(i.e. the concavity) changes.” Below is a tool to help you learn more about inflection points.

WolframAlpha.com's Inflection Points – Easy to use, results include the plotted points.

Newton's Method

Wolfram MathWorld teaches that Newton's Method (or Newton-Raphson) is “a root-finding algorithm that uses the first few terms of the Taylor series of a function in the vicinity of a suspected root.” Below are tools to help you learn how to use Newton's Method:

Keisan.Casio.com's Newton's Method – The Newton's Method formula is provided. Input your function and its derivative to get your results.
Shodor.org's Newton's Method Equation Solver – Quick and easy to use, just enter your function, its derivative, the initial “x” value, and the number of decimal places to be provided in your response and your results will be provided. It also tells you how many iterations were needed to get your response.

WolframAlpha.com's Newton-Raphson Method – Fast and straightforward; the formula is provided.
Maccery.com's Newton's Method – Scroll down to the Newton's Method tool. Enter your data. The results will include each iteration.

Integrals

As Wolfram MathWorld explains, an integral is “a mathematical object that can be interpreted as an area or a generalization of area.” The tools below will help improve your ability to work with integrals:

Calculus-Calculator.com's Integral - Easy to work with and provides a step-by-step explanation along with your results.

WolframAlpha.com's Integral – Learn more about integrals from the tutorial information and examples provided. Results include a graphed representation, the series expansion, and the indefinite integral.

Integral-Calculator.com's Integral - Provides examples to help you get started.

Symbolab.com's Integral – Cleanly designed and includes a step-by-step explanation with results.

MathPortal.org's Integral – Follow the instructions provided to ensure you input your data correctly. Use the “Generate Example” button to learn more about how integrals work.

NumberEmpire.com's Integral – Use one of the four examples provided or enter your own function. Results are easy to interpret.

SolveMyMath.com's Integral – Simple to use and provides clear results.

WebMath.com's Solve an Indefinite Integral – Great for those just getting started with integrals. Best to use this tool with basic integrals only.

Keisan.Casio.com's Exponential Integral – Enter the value of “x” to get started. Results include your function on a graph and a two-step explanation.

CalCul.com's Integral - Enter your expression and your results will be provided.

Had2Know.com's Logarithmic Integral – Tutorial information is provided to help you strengthen your knowledge of integrals. Enter the value of “x” and clear results are provided.

MiniWebTool.com's Exponential Integral – The defining formula is provided as a reference. Enter the value of “x” to get your results.

40 Advanced Calculus Calculators

Riemann Sums

As MathOpenRef.com explains, a Riemann sum is “a method for approximating the total area underneath a curve on a graph, otherwise known as an integral.” Below is a collection of resources to help you better understand Riemann sums.

MathWorld.Wolfram.com's Riemann Sum – Input your data to see your Riemann Sum on a graph. Play around with the inputted data to see how the graph changes.

EMathHelp.net's Riemann Sum – Easy to use and includes a step-by-step explanation with your results.

IntMath.com's Riemann Sums Applet – Tutorial information is provided. Choose a function from the drop down menu to see how it appears on the graph. Adjust the sliders to see how the graphed Riemann Sum changes on the graph.

Trapezoidal Rule

MathWords.com explains that the trapezoidal rule is “a method for approximating a definite integral using linear approximations of f.” The tools below will help you learn how to use the trapezoidal rule.

NastyAccident.com's Trapezoidal Rule – Follow the instructions to enter your data. Results include a step-by-step explanation.

EMathHelp.net's Trapezoidal Rule – Provides a step-by-step explanation with your results.

EasyCalculation.com's Trapezoidal Rule – Learn more about the trapezoidal rule from the provided tutorial information. Follow the instructions provided to ensure you enter your data correctly.

Partial Fraction Decomposition

As PurpleMath.com explains, partial fraction decomposition is “the process of starting with the simplified answer and taking it back apart, or ‘decomposing' the final expression into its initial polynomial fractions.” Below is a collection of resources to help you better understand partial fraction decomposition.

WolframAlpha.com's Partial Fraction Decomposition – Simple and straightforward, just enter the numerator and denominator to get your result.

Calc101.com's Step-by-Step Partial Fractions – Enter your expression (or use the example provided) and then a step-by-step explanation for finding the partial fraction will be provided.

QuickMath.com's Partial Fractions – Quick and easy to use, just enter your function to find the partial fraction. A Basic and Advanced version are provided.

Symbolab.com's Partial Fractions – Enter your expression or use one of the examples provided. A step-by-step explanation will be provided with the results.

Inverse Functions

As Wikipedia.org explains, an inverse function “is a function that ‘reverses' another function.” Below is a collection of tools to help you strengthen your understanding of inverse functions.

Symbolab.com's Inverse Function – Cleanly designed, easy to use, and provides a step-by-step explanation with results. Click “Graph” to see your inverse function on a graph.

WolframAlpha.com's Inverse Function – Simple enough to illustrate the fundamentals, the results include your graphed inverse function.

NumberEmpire.com's Inverse Function – Choose one of the four examples or enter your own function to get the inverse function.

AnalyzeMath.com's Inverse Function – Click the “Show Me” button and this resource will guide you through the four-step process for finding the inverse function.

CalculatorSoup.com's Inverse Function – Use the drop down menu to choose which function you'd like to find. Then, enter the value of “x” to get your results.

Keisan.Casio.com's Inverse Function – Enter the value of “x” and the inverse hyperbolic functions will be provided.

Gyplan.com's Inverse Function – Use the drop down menu to choose the type of inverse function you'd like to find and then enter the value of “x” to get your results.

Differential Equation

As Wolfram MathWorld explains, a differential equation is “an equation that involves the derivatives of a function as well as the function itself.” Below are several tools to help you learn more about differential equations:

WolframAlpha.com's Differential Equations – Use to solve several different kinds of differential equations. Results include the solution, plots of sample individual solutions, the graphed sample solution family, and more.

Symbolab.com's Ordinary Differential Equations – Cleanly designed and easy to use, the results include a step-by-step explanation. Enter your own equation or experiment using the provided examples.

Math-CS.Gordon.edu's First Order Differential Equation Solver – From Gordon College's Department of Mathematics and Computer Science, the equation solver comes with some tutorial information. Results include a graph of the solution.

EasyCalculation.com's Homogenous Differential Equations – Quick, easy to use, and provides clear results.

MathScoop.com's Euler Method – Uses the Euler Method to solve your equation. The results include a Euler Table and a graph of the Euler points.

Keisan.Casio.com's Euler's Method – The needed formula is included, and an Euler table is created with your results.

Had2Know.com's Second Order Differential Equation Solver – Learn more about solving differential equations from the provided tutorial information and explained cases.

Arc Length

MathWords.com teaches that arc length is thelength of a curve or line. Below is a collection of resources to help you find arc length.

1728.org's Arc Length – Choose what you'd like to solve for then enter your known values. Your result will be provided.

HandyMath.com's Complete Circular Arc – Input two known values to find the radius, length, width, height, apothem, angle, and area of an arc or circle segment.

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AJDesigner.com's Circle Arc – A labeled circle diagram and the arc length formula are given. Enter the radius and central angle to get your result.

WolframAlpha.com's Arc Length – This resource will perform several functions related to finding arc length, and it provides an example for each to help you get started.

TutorVista.com's Arc Length – A step-by-step explanation for how to find the arc length and examples with explanations and results are provided.

MathOpenRef.com's Interactive Arc Length – Drag point A or point B to see how the arc length adjusts.

Flexibility.com's Arc Length – Choose which option to use for finding arc length based on your known values. A labeled circle diagram is given as a visual aid.

PlanetCalc.com's Arc Length – A labeled circle diagram and formulas are provided. Enter the radius and angle to find the arc length and other properties, such as area, chord length, and perimeter.

EasyCalculation.com's Arc Length – Enter your radius and angle and the arc length will be provided.

Center of Mass

MathWords.com provides the formulas for finding Center of Mass. Below is a collection of tools to help strengthen your understanding of center of mass.

TutorVista.com's Center of Mass – Enter the “different value of masses” and the “distance of the respective masses” to find the center of mass.

Calculator.Swiftutors.com's Center of Mass – Provides tutorial information, very uncomplicated and easy for any student to navigate.

LearningAboutElectronics.com's Center of Mass – Tutorial information, a labeled diagram and instructions on using the tool are provided. Enter all known masses and their respective distances to find the center of mass.

Sequences

As Paul's Online Math Notes explains, a sequence is “a list of numbers written in a specific order.” The tool below will help you learn more about sequences:

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WolfamAlpha.com's Sequences – Examples are provided to show how to use this resource based on different sequences criteria. Results include a graphed representation, a table of values, and the series representations.

Series

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As MathOpenReference.com explains, a series is “the sum of some set of terms of a sequence.” Use the resources below to strengthen your understanding of series.

NumberEmpire.com's Series – Use one of the four provided examples or enter your own expression. Results are easy to interpret and offer the option to edit your expression.

MathScoop.com's Geometric Series – Simple and swift, just enter your values and the sum will be provided.

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CalCul.com's Geometric Series – Adjust the variable values using the arrows and the result will be provided instantly.