Interpolation Calculator Online

Method

Find y at x =

Decimal places

Inverse Lagrangegiven y, find x

Data table

4 points · equal spacing, h = 3

i	xᵢ	yᵢ or f(xᵢ)	Action
0
1
2
3

x: 20 23 26 29 y: 0.342 0.3907 0.4384 0.4848

Paste or edit data

Given data

i	0	1	2	3
xᵢ	20	23	26	29
yᵢ	0.342	0.3907	0.4384	0.4848

Method

Newton's Forward Interpolation. x = 21 is nearer the beginning of the table, so Newton's Forward formula is used.

Forward difference table

x	y	Δ	Δ²	Δ³
20	0.342
		0.0487 Δy₀ = y₁ − y₀ = 0.3907 − 0.342 = 0.0487
23	0.3907		-0.001 Δ²y₀ = Δy₁ − Δy₀ = 0.0477 − 0.0487 = -0.001
		0.0477 Δy₁ = y₂ − y₁ = 0.4384 − 0.3907 = 0.0477		-0.0003 Δ³y₀ = Δ²y₁ − Δ²y₀ = -0.0013 − -0.001 = -0.0003
26	0.4384		-0.0013 Δ²y₁ = Δy₂ − Δy₁ = 0.0464 − 0.0477 = -0.0013
		0.0464 Δy₂ = y₃ − y₂ = 0.4848 − 0.4384 = 0.0464
29	0.4848

Highlighted cells are the diagonal used in the formula.

How table values are calculated

Δ = 0.0487

Δy₀ = y₁ − y₀ = 0.3907 − 0.342 = 0.0487

Δ = 0.0477

Δy₁ = y₂ − y₁ = 0.4384 − 0.3907 = 0.0477

Δ = 0.0464

Δy₂ = y₃ − y₂ = 0.4848 − 0.4384 = 0.0464

Δ² = -0.001

Δ²y₀ = Δy₁ − Δy₀ = 0.0477 − 0.0487 = -0.001

Δ² = -0.0013

Δ²y₁ = Δy₂ − Δy₁ = 0.0464 − 0.0477 = -0.0013

Δ³ = -0.0003

Δ³y₀ = Δ²y₁ − Δ²y₀ = -0.0013 − -0.001 = -0.0003

Values used from table

y₀

0.342

Δy₀

0.0487

Δ²y₀

-0.001

Δ³y₀

-0.0003

0.3333

Compute u

u = (x − x₀) / h

u = (21 − 20) / 3

u = 0.3333

h = 3 (common difference of x-values).

Interpolation formula

y = f(x) = y₀ + u·Δy₀

+ [u(u−1) / 2!] · Δ²y₀

+ [u(u−1)(u−2) / 3!] · Δ³y₀

Substitute the values

y = 0.342 + (0.3333)(0.0487)

+ [0.3333(0.3333−1) / 2!] · (-0.001)

+ [0.3333(0.3333−1)(0.3333−2) / 3!] · (-0.0003)

Add the terms

Term 0 = y₀ = 0.342

Term 1 = u * Δy₀ = 0.3333 * 0.0487 = 0.016233

Term 2 = [0.3333 * (0.3333−1) / 2!] * Δ²y₀ = [0.3333 * (0.3333−1) / 2!] * -0.001 = 0.000111

Term 3 = [0.3333 * (0.3333−1) * (0.3333−2) / 3!] * Δ³y₀ = [0.3333 * (0.3333−1) * (0.3333−2) / 3!] * -0.0003 = -0.000019

y = 0.342 + 0.016233 + 0.000111 − 0.000019

y = 0.3583

Answer

y(21) = 0.3583

Tip: use samples, upload, copy, download, and send-to actions inside the workspace where available.

What is Interpolation Calculator?

Interpolation Calculator is a free, browser-based tool that helps you get the job done quickly. Step-by-step Newton forward/backward, divided difference & Lagrange interpolation with full tables. It's built for speed and privacy: Everything runs locally in your browser — your data is never uploaded to a server. No sign-up, no installs, and no daily limits.

How to use Interpolation Calculator

1Paste or drop your data into the workspace.
2Adjust the available options to suit your data.
3Copy or download the result — it never leaves your browser.

Features

Fast, focused, and easy to use
100% client-side — no upload, fully private
Free with no account, no watermark, and no daily limit
Works on large inputs, limited only by your device's memory
Load a sample, then copy, download, or share your result

Common uses

Quick one-off data jobs without opening a heavy app
Preparing data before importing it elsewhere
Sharing a reproducible result with a teammate via a link

Used by

Students
Finance teams
Operations teams
Analysts

Examples

Example 1

Example input

Goal: calculate a interpolation calculator result
Values: sample amount, rate, and time period

Example output

The calculator shows the final value, intermediate figures, and any percentage or difference used in the result.

Example 2

Simple case

A small input for Interpolation Calculator

Immediate result

A focused result you can review before copying or downloading.

Example 3

Custom case

Input with changed settings or options

Adjusted result

The output updates to match your selected options.

Example 4

Review case

A value you want to double-check before using elsewhere

Reviewable output

The result gives you a safer handoff into the next task.

Example 5

Workflow case

Input prepared by another DataXForge tool

Next-step result

The output can be copied, downloaded, or used in another browser workflow.

Common errors

Input is copied from a source with hidden whitespace or encoding issues.
The result is not reviewed before being reused elsewhere.
The wrong options are selected for the target workflow.
The original data is not kept for comparison.

How it works

1Accepts the input for Interpolation Calculator.
2Runs the operation in the browser.
3Returns a result you can copy, download, or continue using.

Recommended workflow

1
Prepare the input
Use this tool as the focused step in a larger browser-based workflow.
2
Run Interpolation Calculator
Review the preview, copy or download the result, and keep everything local in your browser.
3
Next recommended tool
System of Linear Equations: Solve linear systems with RREF, Gauss-Jacobi, and Gauss-Seidel methods using full step-by-step tables.
Open tool
4
Then continue with
Scientific Calculator: Trig, log, exp, powers — expression evaluator.
Open tool
5
Then continue with
Mean / Median / Mode: Central tendency for numeric columns.
Open tool

Frequently asked questions

How do I use Interpolation Calculator?: Paste or drop your data into the workspace, adjust the options to fit your data, then copy or download the result. Step-by-step Newton forward/backward, divided difference & Lagrange interpolation with full tables.
Is my data uploaded or stored anywhere?: No. Everything runs locally in your browser — your data is never uploaded to a server. Nothing is sent to a server, so it's safe to use with private or sensitive data.
Is Interpolation Calculator free?: Yes — it's completely free with no account, no sign-up, no watermark, and no daily usage limits.
What's the maximum file size?: There's no hard limit imposed by the tool. Because processing happens in your browser, the practical ceiling is your device's available memory — most everyday files work instantly.
Do I need to install anything?: No installs and no extensions — it runs entirely in your web browser and even works offline once the page has loaded.

xᵢ

yᵢ or f(xᵢ)

Action

xᵢ

yᵢ

0.342

0.3907

0.4384

0.4848

Δ²

Δ³

0.342

0.0487

Δy₀ = y₁ − y₀ = 0.3907 − 0.342 = 0.0487

0.3907

-0.001

Δ²y₀ = Δy₁ − Δy₀ = 0.0477 − 0.0487 = -0.001

0.0477

Δy₁ = y₂ − y₁ = 0.4384 − 0.3907 = 0.0477

-0.0003

Δ³y₀ = Δ²y₁ − Δ²y₀ = -0.0013 − -0.001 = -0.0003

0.4384

-0.0013

Δ²y₁ = Δy₂ − Δy₁ = 0.0464 − 0.0477 = -0.0013

0.0464

Δy₂ = y₃ − y₂ = 0.4848 − 0.4384 = 0.0464

0.4848

What is Interpolation Calculator?

Examples

Example 1

Example input

Goal: calculate a interpolation calculator result
Values: sample amount, rate, and time period

Example output

The calculator shows the final value, intermediate figures, and any percentage or difference used in the result.

Example 2

Simple case

A small input for Interpolation Calculator

Immediate result

A focused result you can review before copying or downloading.

Example 3

Custom case

Input with changed settings or options

Adjusted result

The output updates to match your selected options.

Example 4

Review case

A value you want to double-check before using elsewhere

Reviewable output

The result gives you a safer handoff into the next task.

Example 5

Workflow case

Input prepared by another DataXForge tool

Next-step result

The output can be copied, downloaded, or used in another browser workflow.

Recommended workflow

Prepare the input

Use this tool as the focused step in a larger browser-based workflow.

Run Interpolation Calculator

Review the preview, copy or download the result, and keep everything local in your browser.

Next recommended tool

System of Linear Equations: Solve linear systems with RREF, Gauss-Jacobi, and Gauss-Seidel methods using full step-by-step tables.

Open tool

Then continue with

Scientific Calculator: Trig, log, exp, powers — expression evaluator.

Open tool

Then continue with

Mean / Median / Mode: Central tendency for numeric columns.

Open tool

Frequently asked questions

How do I use Interpolation Calculator?

Paste or drop your data into the workspace, adjust the options to fit your data, then copy or download the result. Step-by-step Newton forward/backward, divided difference & Lagrange interpolation with full tables.

Is my data uploaded or stored anywhere?

No. Everything runs locally in your browser — your data is never uploaded to a server. Nothing is sent to a server, so it's safe to use with private or sensitive data.

Is Interpolation Calculator free?

Yes — it's completely free with no account, no sign-up, no watermark, and no daily usage limits.

What's the maximum file size?

There's no hard limit imposed by the tool. Because processing happens in your browser, the practical ceiling is your device's available memory — most everyday files work instantly.

Do I need to install anything?

No installs and no extensions — it runs entirely in your web browser and even works offline once the page has loaded.