01
Formula
M = P · r / (1 − (1 + r)⁻ⁿ)
The equation is on the page, with your values substituted, so a result can be reproduced by hand.
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The verifiable calculator library · Finance & engineering
Every calculator should show its work.
372 finance and engineering instruments — from mortgage payments to hypersonic reentry — each with its formula, its source and a worked example. All of it computed on your device.
No account. No uploads. 186 cited sources.Free core, Pro analysis
Mortgage / paymentLive · local
Monthly payment$2,001.62
Total interest$400,583Total paid$720,583
Principal, rate and term only — taxes and insurance are separate.
01 — Inside one instrument
The tool, not a diagram of the tool.
Not a screenshot — the instrument itself, running on this page. Move a slider and the answer, the schedule and the charts recompute in front of you. Switch between finance and engineering; the shell is identical.
01Inputs
Price, down payment, rate, term, property tax, insurance and HOA — every one live.
02Answer
The PITI figure first, with the principal-and-interest split beside it.
03Evidence
Amortisation table, balance curve, term comparison and the formula panel.
02 — Anatomy of a result
A number, a method, and a receipt.
The instrument above is not a mock-up. It is the same engine the mortgage page runs — and it keeps its working visible.
02
Source
Broverman — Mathematics of Investment and Credit
Every instrument names the work its method comes from: 186 primary texts, papers and standards across the library.
03
Worked example
$320,000 at 6.40% over 30 years → $2,001.62 / month
A concrete case with real numbers, so you can tell whether the tool is answering the question you actually asked.
03 — Provenance
Every instrument cites its source.
186primary works, from Portfolio Selection to the NIST Handbook.
Read the citation index- Portfolio Selection, 1952
- Option pricing, 1973
- Term structure, 1992
- Stochastic volatility, 1993
- American options, 2001
- Mechanics of Materials
- Heat and Mass Transfer
- The Finite Element Method
- Reference standards
Implements
- IRS Rev. Proc. 2025-32
- IRS Notice 2025-67
- NIST SP 800-186
- NFPA 70 · NEC 310.16
- ISO 6946
- ASTM B258
- NACA Report 1135
Reviewed October 2026 · every formula on the page, not just in the docs
04 — Start from the question
Bring a decision, not a keyword.
Finance
Should I refinance?
Compare the new payment, the break-even month and the lifetime interest against staying put.
Refinance CalculatorMarketsWhat is this option worth?
Price a European call or put from spot, strike, volatility and time — with the Greeks in view.
Black–Scholes Options CalculatorEngineeringWill this beam hold?
Deflection, bending stress and section capacity for a simply supported span under load.
Beam Deflection & Stress Calculator05 — The instrument atlas
One workspace, 372 instruments.
12 of them, each with the curve it actually produces. The same interface whether you are amortising a loan or solving a re-entry heat shield — 179 finance, 193 engineering.
Finance
179 instruments01 · MoneyAmortization
Mortgage
Balance, payment and lifetime interest across a 30-year term — the curve every extra payment bends.
Open instrument02 · MarketsFixed income
Bond yield
Clean price against yield for a 5% ten-year bond. Convexity you can see, not just read about.
Open instrument03 · MarketsDerivatives
Options payoff
Call payoff at expiry with the strike at 100 — the shape underneath every pricing model.
Open instrument04 · MarketsValuation
DCF valuation
Enterprise value against WACC for a five-year FCFF forecast — the slope that decides the deal.
Open instrument05 · MoneyRetirement
Retirement
Accumulation to 65, then a 4% draw rising with inflation — the shape of the whole plan.
Open instrument06 · MoneyGrowth
Compound interest
Monthly contributions compounding at 7% — the curve behind every savings plan.
Open instrumentEngineering
193 instruments01 · EngineeringStructures
Beam deflection
Deflected shape of a simply supported span under uniform load, from w, L and EI.
Open instrument02 · EngineeringDynamics
Projectile motion
A 45° launch at 30 m/s from a 6 m platform — range, apex and time of flight without drag.
Open instrument03 · EngineeringSignals
Signal spectrum
A two-tone waveform, exactly the input the discrete Fourier transform instrument decomposes.
Open instrument04 · EngineeringThermal
Heat exchanger
LMTD against the cold-outlet temperature for a 150→90 °C hot stream.
Open instrument05 · EngineeringStructures
Column buckling
Critical load against column length — the 1/L² that makes slenderness decisive.
Open instrument06 · EngineeringReliability
Weibull reliability
Survival against time for β = 1.8 — wear-out you can read off the curve.
Open instrumentInside
- Engineering104
- Finance87
- Structures29
- Fluids15
- Thermal14
- Electrical11
- Debt11
- Mechanical9
- Fixed income9
- Tax8
- Retirement7
- Growth7
372instruments
186primary sources
0uploads
1requirement — a browser
06 — Recently reviewed
Checked, dated, on the record.
Every instrument carries the date a human last checked its math against the source.
07 — Who it is for
One library, read at your depth.
The same engine answers a household budget and a Heston surface. Pick the shelf that matches the question — the method, the source and the assumptions travel with it.
For households
Everyday money decisions
What the payment really is, what refinancing saves, and how fast a balance falls when one extra payment goes out.
Browse the shelfFor students
Coursework with the working shown
Every result carries its formula, substitution and source — so a number can be reproduced by hand, not just copied.
Browse the shelfFor engineers
Design checks, not black boxes
Beam, column, thermal and fluid checks with the governing equation, assumptions and units exposed on the page.
Browse the shelfFor analysts
Valuation and market structure
From a DCF and WACC to bond duration, option pricing and portfolio construction — the same audit trail at every step.
Browse the shelfFor researchers
Models you can inspect
Stochastic volatility, GARCH, Monte Carlo, FEM and plasticity — with the discretisation and closure choices named.
Browse the shelfFor teams and industry
Risk, throughput and scale
VaR, credit hazard, consensus latency and channel capacity for decisions that have to survive an audit.
Browse the shelf08 — What stays true
Built to be checked.
The core answer is free
Every instrument’s primary calculation, inputs and result are open without an account. Advanced analysis is packaged separately; nothing on a free instrument is gated.
It runs on your device
No network calls after the page loads. Your loan balance, your portfolio, your beam dimensions never leave the tab.
The method is on the page
Each result carries its formula, the source it came from, and a worked example you can check by hand.
09 — Questions
The short answers.
Still deciding? The method pages show how every result is produced, and where each formula comes from.
Read the methodAre these calculators really free?
Yes. Every core calculation is free and needs no account, no trial and no card. Pro and Ultra packaging exists for advanced analysis on instruments that support it — the primary answer on every instrument stays open.
Do my numbers leave my device?
No. All math runs in your browser using JavaScript and web workers. Values you type are never uploaded, and there is no server-side calculation to log them.
How do I know the results are right?
Each instrument shows the formula it uses, cites the primary source, and includes a worked example. Where a standard publishes reference values, the implementation is checked against them.
How is this different from the calculator in a search result?
Most calculators return a number and stop. ZorvLabs returns the number, the method behind it, and the assumption you would need to change to get a different answer.
Pick an instrument.
See the math.
Open any of the 372 calculators and change a number — the method, the source and the result move with you.
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